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Geometric Invariant Theory gives a method for constructing quotients for group actions on algebraic varieties which in many cases appear as moduli spaces parametrizing isomorphism classes of geometric objects (vector bundles, polarized…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…
We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.
Applying geometric methods of $2$-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite…
We prove that if $G$ is finite 2-generated $p$-group of nilpotence class at most 2 then the group algebra of $G$ with coefficients in the field with $p$ elements determines $G$ up to isomorphisms.
In this short note we construct two families of examples of large stratifying systems in module categories of algebras. The first examples consists on stratifying systems of infinite size in the module category of an algebra $A$. In the…
We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras.
If a morphism of germs of schemes induces isomorphisms of all local jet schemes, does it follow that the morphism is an isomorphism? This problem is called the local isomorphism problem. In this paper, we use jet schemes to introduce…
We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation.…
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective,…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.
We study finiteness conditions on essential extensions of simple modules over the quantum plane, the quantized Weyl algebra and Noetherian down-up algebras. The results achieved improve the ones obtained in [arXiv:0906.2930] for down-up…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
For any integral lattice $Q$, one can construct a vertex algebra $V_Q$ called a lattice vertex algebra. If $\sigma$ is an automorphism of $Q$ of finite order, it can be lifted to an automorphism of $V_Q$. In this paper we classify the…
The goal of this paper is to present a number of problems about automorphism groups of nonpositively curved polyhedral complexes and their lattices, meant to highlight possible directions for future research.
The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring $R$. This, in particular, generalises the group of quadratic algebras (free or projective), which…
Given a noether algebra with a noncommutative resolution, a general construction of new noncommutative resolutions is given. As an application, it is proved that any finite length module over a regular local or polynomial ring gives rise,…
This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.