Published volumes
19521968 Revista de la Unión Matemática Argentina y de la Asociación Física Argentina
19441951 Revista de la Unión Matemática Argentina; órgano de la Asociación Física Argentina
19361944

Volume 59, number 1 (2018)
June 2018
Front matter

Comparison morphisms between two projective
resolutions of monomial algebras.
María Julia Redondo and Lucrecia Román
We construct comparison morphisms between two wellknown projective
resolutions of a monomial algebra $A$: the bar resolution
$\operatorname{\mathbb{Bar}} A$ and Bardzell's resolution
$\operatorname{\mathbb{Ap}} A$; the first one is used to define the
cup product and the Lie bracket on the Hochschild cohomology
$\operatorname{HH} ^*(A)$ and the second one has been shown to be an
efficient tool for computation of these cohomology groups. The
constructed comparison morphisms allow us to show that the cup
product restricted to even degrees of the Hochschild cohomology has a
very simple description. Moreover, for $A= \mathbb{k} Q/I$ a monomial
algebra such that $\dim_ \mathbb{k} e_i A e_j = 1$ whenever there
exists an arrow $\alpha: i \to j \in Q_1$, we describe the Lie action
of the Lie algebra $\operatorname{HH} ^1(A)$ on $\operatorname{HH} ^
{\ast} (A)$.

1–31 
The group of automorphisms of the moduli space of
principal bundles with structure group $F_4$ and $E_6$.
Álvaro Antón Sancho
Let $X$ be a smooth complex projective irreducible curve of genus $g
\geq 3$. Let $G$ be the simple complex exceptional Lie group $F_4$ or
$E_6$ and let $M(G)$ be the moduli space of principal $G$bundles. In
this work we describe the group of automorphisms of $M(G)$. In
particular, we prove that the only automorphisms of $M(F_4)$ are those
induced by the automorphisms of the base curve $X$ by pullback and
that the automorphisms of $M(E_6)$ are combinations of the action of
the automorphisms of $X$ by pullback, the action of the only
nontrivial outer involution of $E_6$ on $M(E_6)$ by taking the dual and
the action of the third torsion of the Picard group of $X$ by tensor
product. We also prove a Torelli type theorem for the moduli spaces of
principal $F_4$ and $E_6$bundles, which we use as an auxiliary result
in the proof of the main theorems, but which is interesting in itself.
We finally draw some conclusions about the way we can see the natural
map $M(F_4) \rightarrow M(E_6)$ induced by the inclusion of groups $F_4
\hookrightarrow E_6$.

33–56 
A note on wavelet expansions for dyadic BMO functions
in spaces of homogeneous type.
Raquel Crescimbeni and Luis Nowak
We give a characterization of dyadic BMO spaces in terms of Haar
wavelet coefficients in spaces of homogeneous type.

57–72 
Interior $L^p$estimates and local $A_p$weights.
Isolda Cardoso, Pablo Viola, and Beatriz Viviani
Let $\Omega$ be a nonempty open proper and connected subset of $
\mathbb R^ {n} $, $n \geq 3$. Consider the elliptic Schrödinger type
operator $L_ {E} u= A_ {E} u+Vu=  \Sigma_{ij} a_ {ij} (x) u_ {x_i
x_j} +Vu$ in $ \Omega$, and the linear parabolic operator $L_ {P}
u=A_ {P} u+Vu=$ $u_ {t}  \Sigma a_ {ij} (x,t)u_ {x_{i}x_{j}} +Vu$ in
$ \Omega_{T} = \Omega \times (0,T)$, where the coefficients $a_ {ij}
\in \mathrm{VMO} $ and the potential $V$ satisfies a reverse Hölder
condition. The aim of this paper is to obtain a priori estimates for
the operators $L_ {E} $ and $L_ {P} $ in weighted Sobolev spaces
involving the distance to the boundary and weights in a local $A_ {p}
$ class.

73–98 
A unified point of view on boundedness of Riesz type potentials.
Bibiana Iaffei and Liliana Nitti
We introduce a natural extension of the Riesz potentials to
quasimetric measure spaces with an upper doubling measure. In
particular, these operators are defined when the underlying space
has components of differing dimensions. We study the behavior of
the potential on classical and variable exponent Lebesgue spaces,
obtaining necessary and sufficient conditions for its boundedness.
The technique we use relies on a geometric property of the measure
of the balls which holds both in the doubling and nondoubling
situations, and allows us to present our results in a unified way.

99–121 
$T^*$extensions and abelian extensions of homLie color algebras.
Bing Sun, Liangyun Chen, and Yan Liu
We study homNijenhuis operators, $T^ \ast$extensions and abelian
extensions of homLie color algebras. We show that the infinitesimal
deformation generated by a homNijenhuis operator is trivial. Many
properties of a homLie color algebra can be lifted to its $T^
\ast$extensions such as nilpotency, solvability and decomposition.
It is proved that every finitedimensional nilpotent quadratic
homLie color algebra over an algebraically closed field of
characteristic not 2 is isometric to a $T^ \ast$extension of a
nilpotent Lie color algebra. Moreover, we introduce abelian
extensions of homLie color algebras and show that there is a
representation and a 2cocycle, associated to any abelian extension.

123–142 
An application of Pappus' Involution Theorem to
Cayley–Klein projective models.
Rubén Vigara
Pappus' Involution Theorem is useful for proving incidence
relations in the hyperbolic and elliptic planes. This fact is
exemplified with the proof of a theorem about a family of 4gons
in the hyperbolic and elliptic planes. This nonEuclidean theorem
is also reinterpreted in multiple ways, providing some other
theorems for different figures in the hyperbolic plane.

143–156 
A notion of compatibility for Armendariz and Baer
properties over skew PBW extensions.
Armando Reyes and Héctor Suárez
In this paper we are interested in studying the properties of
Armendariz, Baer, quasiBaer, p.p. and p.q.Baer over skew PBW
extensions. Using a notion of compatibility, we generalize several
propositions established for Ore extensions and present new results
for several noncommutative rings which can not be expressed as Ore
extensions (universal enveloping algebras, diffusion algebras, and
others).

157–178 
Metallic conjugate connections.
Adara M. Blaga and CristinaElena Hrețcanu
Properties of metallic conjugate connections are stated by pointing
out their relation to product conjugate connections. We define the
analogous in metallic geometry of the structural and the virtual
tensors from the almost product geometry and express the metallic
conjugate connections in terms of these tensors. From an applied
point of view we consider invariant distributions with respect to the
metallic structure and for a natural pair of complementary
distributions, the above structural and virtual tensors are expressed
in terms of O'Neill–Gray tensor fields.

179–192 
On partial orders in proper $*$rings.
Janko Marovt
We study orders in proper $*$rings that are derived from the
corenilpotent decomposition. The notion of the CNstar partial
order and the Sstar partial order is extended from $M_ {n} (
\mathbb{C)} $, the set of all $n \times n$ complex matrices, to the
set of all Drazin invertible elements in proper $*$rings with
identity. Properties of these orders are investigated and their
characterizations are presented. For a proper $*$ring $ \mathcal{A}
$ with identity, it is shown that on the set of all Drazin invertible
elements $a \in \mathcal{A} $ where the core part of $a$ is an EP
element, the CNstar partial order implies the star partial order.

193–204 
Volume 59, number 2 (2018)
December 2018
Front matter

QHWM of the orthogonal and symplectic types Lie subalgebras of the Lie
algebra of the matrix quantum pseudo differential operators.
Karina Batistelli and Carina Boyallian
In this paper we classify the irreducible quasifinite highest weight
modules over the orthogonal and symplectic types Lie subalgebras of
the Lie algebra of the matrix quantum pseudodifferential operators.
We also realize them in terms of the irreducible quasifinite highest
weight modules of the Lie algebras of infinite matrices with finitely
many nonzero diagonals and its classical Lie subalgebras of types B,
C and D.

205–240 
Cyclic groups with the same Hodge series.
Daryl R. DeFord and Peter G. Doyle
The Hodge series of a finite matrix group is the generating function
for invariant exterior forms of specified order $p$ and degree $k$.
Lauret, Miatello, and Rossetti gave examples of pairs of
nonconjugate cyclic groups having the same Hodge series; the
corresponding space forms are isospectral for the Laplacian on
$p$forms for all $p$, but not for all natural operators. Here we
explain, simplify, and extend their investigations.

241–254 
Remarks on Liouvilletype theorems on complete noncompact Finsler manifolds.
Songting Yin and Pan Zhang
We give a gradient estimate of the positive solution to the equation
\[ \Delta u= \lambda^2u, \quad \lambda \geq 0 \] on a complete
noncompact Finsler manifold. Then we obtain the corresponding
Liouvilletype theorem and Harnack inequality for the solution.
Moreover, on a complete noncompact Finsler manifold we also prove a
Liouvilletype theorem for a $C^2$nonnegative function $f$
satisfying \[ \Delta f \geq cf^d, \quad c>0, \; d>1, \] which
improves a result obtained by Yin and He.

255–264 
A topological duality for mildly distributive meetsemilattices.
Sergio A. Celani and Luciano J. González
We develop a topological duality for the category of mildly
distributive meetsemilattices with a top element and certain
morphisms between them. Then, we use this duality to characterize
topologically the lattices of Frink ideals and filters, and we also
obtain a topological representation for some congruences on mildly
distributive meetsemilattices.

265–284 
A reduction formula for lengthtwo polylogarithms and some applications.
Matilde N. Lalín and JeanSébastien Lechasseur
We use shuffle and stuffle relations to give a simple proof of a
reduction formula for lengthtwo multiple polylogarithms evaluated in
complex parameters of absolute value 1 in terms of a finite sum of
products of lengthone polylogarithms. This result was originally due
to Nakamura and recently reproved by Panzer by different methods.
This generalises results of Borwein and Girgensohn for alternating
Euler sums and for multiple zeta values twisted by fourth roots of
unity by the first author. We also explore implications for other
colored multiple zeta values and present some applications to Mahler
measure and Feynman diagrams.

285–309 
The shape derivative of the Gauss curvature.
Aníbal ChiccoRuiz, Pedro Morin, and M. Sebastian Pauletti
We present a review of results about the shape derivatives of scalar
and vectorvalued shape functions, and extend the results from Doğan
and Nochetto [ESAIM Math. Model. Numer. Anal.
46 (2012), no. 1, 5979] to more general surface energies. In that
article, Doğan and Nochetto consider surface energies defined
as integrals over surfaces of functions that can depend on the
position, the unit normal and the mean curvature of the surface. In
this work we present a systematic way to derive formulas for the
shape derivative of more general geometric quantities, including the
Gauss curvature (a new result not available in the literature) and
other geometric invariants (eigenvalues of the second fundamental
form). This is done for hypersurfaces in the Euclidean space of any
finite dimension. As an application of the results, with relevance
for numerical methods in applied problems, we derive a Newtontype
method to approximate a minimizer of a shape functional. We finally
find the particular formulas for the first and second order shape
derivatives of the area and the Willmore functional, which are
necessary for the aforementioned Newtontype method.

311–337 
A HardyLittlewood maximal operator adapted to the harmonic oscillator.
Julian Bailey
This paper constructs a Hardy–Littlewood type maximal operator
adapted to the Schr ö dinger operator $ \mathcal{L} :=  \Delta +
x^2$ acting on $L^ {2} ( \mathbb{R} ^ {d} )$. It achieves this
through the use of the Gaussian grid $ \Delta^{\gamma} _ {0} $,
constructed by Maas, van Neerven, and Portal [Ark. Mat. 50
(2012), no. 2, 379395] with the OrnsteinUhlenbeck operator in
mind. At the scale of this grid, this maximal operator will resemble
the classical Hardy–Littlewood operator. At a larger scale, the
cubes of the maximal function are decomposed into cubes from $
\Delta^{\gamma} _ {0} $ and weighted appropriately. Through this
maximal function, a new class of weights is defined, $A_ {p} ^ {+} $,
with the property that for any $w \in A_{p} ^ {+} $ the heat maximal
operator associated with $ \mathcal{L} $ is bounded from $L^ {p} (w)$
to itself. This class contains any other known class that possesses
this property. In particular, it is strictly larger than $A_ {p} $.

339–373 
Families of transitive maps on $\Bbb{R}$ with horizontal asymptotes.
Bladismir Leal, Guelvis Mata, and Sergio Muñoz
We will prove the existence of a class of transitive maps on the real
line $ \mathbb{R} $, with a discontinuity and horizontal asymptotes,
whose set of periodic orbits is dense in $ \mathbb{R} $; that is, a
class of chaotic families. In addition, we will show a rare
phenomenon: the existence of periodic orbits of period three prevents
the existence of transitivity.

375–387 
Combinatorial and modular solutions of some sequences with links to a
certain conformal map.
Pablo A. Panzone
If $f_n$ is a free parameter, we give a combinatorial closed form
solution of the recursion \[ (n+1)^2 u_ {n+1} f_n u_nn^2 u_ {n1}
=0, \quad n \geq 1, \] and a related generating function. This is
used to give a solution to the Apéry type sequence \[ r_n n^3+r_
{n1} \left \{ \alpha n^3 \frac{3\alpha}{2} n^2+ \left \{
\frac{\alpha}{2} +2 \theta \right \} n \theta \right \} +r_ {n2}
(n1)^3=0, \quad n \geq 2, \] for certain parameters $ \alpha,
\theta$. We show from another viewpoint two independent solutions of
the last recursion related to certain modular forms associated with a
problem of conformal mapping: Let $f( \tau)$ be a conformal map of a
zeroangle hyperbolic quadrangle to an open half plane with values
$0$, $ \rho$, $1$, $ \infty$ ($0< \rho<1$) at the cusps and
define $t=t( \tau): = \frac{1}{\rho} f( \tau)
\frac{f(\tau)\rho}{f(\tau)1} $. Then the function \[ E( \tau)=
\frac{1}{2\pi i} \frac{f'(\tau)}{f(\tau)}
\frac{1}{1\frac{f(\tau)}{\rho}} \] is a solution, as a generating
function in the variable $t$, of the above recurrence. In other
words, $E( \tau)=r_0+r_1t+r_2 t^2+ \dots$, where $r_0=1$, $r_1=
\theta$, $ \alpha=2 \frac{4}{\rho} $.

389–414 
Questions and conjectures on extremal Hilbert series.
Ralf Fröberg and Samuel Lundqvist
Given an ideal of forms in an algebra (polynomial ring, tensor
algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we
consider the Hilbert series of the factor ring. We concentrate on the
minimal Hilbert series, which is achieved when the forms are generic.
In the polynomial ring we also consider the opposite case of maximal
series. This is mainly a survey article, but we give a lot of
problems and conjectures. The only novel results concern the maximal
series in the polynomial ring.

415–429 
Generalizations of hyperbolic area for topological surfaces.
AldoHilario CruzCota
We introduce two generalizations of hyperbolic area for connected,
closed, orientable surfaces: the complexity and the simple complexity
of a surface. These concepts are defined in terms of collections of
branched coverings $M \to \mathbb{P} ^1$, where $M$ is a Riemann
surface homeomorphic to $S$ and $ \mathbb{P} ^1$ is the Riemann
sphere. We prove that if $S$ is a surface of positive genus, then
both the topological complexity and the simple topological complexity
of $S$ are linear functions of its genus.

431–441 
On families of Hopf algebras without the dual Chevalley property.
Naihong Hu and Rongchuan Xiong
Let $ \mathbb{k} $ be an algebraically closed field of characteristic
zero. We construct several families of finitedimensional Hopf
algebras over $ \mathbb{k} $ without the dual Chevalley property via
the generalized lifting method. In particular, we obtain 14 families
of new Hopf algebras of dimension 128 with nonpointed duals which
cover the eight families obtained in our unpublished version,
arXiv:1701.01991 [math.QA].

443–469 
On generalized Jordan prederivations and generalized prederivations of Lie
color algebras.
Chenrui Yao, Yao Ma, and Liangyun Chen
In this paper, the concepts of (generalized) $( \theta,
\varphi)$prederivations and (generalized) Jordan $( \theta,
\varphi)$prederivations on a Lie color algebra are introduced. It is
proved that Jordan $( \theta, \varphi)$prederivations (resp.
generalized Jordan $( \theta, \varphi)$prederivations) are $(
\theta, \varphi)$prederivations (resp. generalized $( \theta,
\varphi)$prederivations) on a Lie color algebra under some
conditions. In particular, Jordan $ \theta$prederivations are $
\theta$prederivations on a Lie color algebra.

471–483 
