Related papers: Abelian Theory
We show that any normal algebraic monoid is an extension of an abelian variety by a normal affine algebraic monoid. This extends (and builds on) Chevalley's structure theorem for algebraic groups.
We obtain a presentation of certain affine q-Schur algebras in terms of generators and relations. The presentation is obtained by adding more relations to the usual presentation of the quantized enveloping algebra of type affine gl_n. Our…
We provide a motivated introduction to the theory of categorical actions of groups and the local geometric Langlands program. Along the way we emphasize applications, old and new, to the usual representation theory of reductive and affine…
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-). Moreover, we obtain a simple set of axioms for the universal part of the theory of such structures. Finally, we prove that…
The algebraic part of approach to groupoids started by S. Zakrzewski is presented.
We give a detailed description of the torsors that correspond to multiloop algebras. These algebras are twisted forms of simple Lie algebras extended over Laurent polynomial rings. They play a crucial role in the construction of Extended…
Torsion theories play an important role in abelian categories and they have been widely studied in the last sixty years. In recent years, with the introduction of pretorsion theories, the definition has been extended to general…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
In this paper we discuss large cardinals and compactness theorems in abelian group theory. More specifically, we generalize two classical compactness results for free abelian groups to the broader context of direct sums of cyclic groups.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…
Let p be a fixed prime. An Abelian p-group is an Abelian group (not necessarily finitely generated) in which every element has for its order some power of p. The countable Abelian p-groups are classified by Ulm's theorem, and Khisamiev…
We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
We start with $n$-torsions in the Jacobian of an $m$-gonal curve and produce $n$-torsions in the class group of certain number field $K$.
Given a group $G$ and an integer $n\geq2$ we construct a new group $\tilde{{\cal K}}(G,n)$. Although this construction naturally occurs in the context of finding new invariants for complex algebraic surfaces, it is related to the theory of…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…