Related papers: Golod-Shafarevich groups: a survey

This is a survey paper of the theory of crystal bases, global bases and the cluster algebra structure on the quantum coordinate rings.

This article will explore the K- and L-theory of group rings and their applications to algebra, geometry and topology. The Farrell-Jones Conjecture characterizes K- and L-theory groups. It has many implications, including the Borel and…

Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on…

This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory…

We survey new results on finite groups of birational transformations of algebraic varieties.

We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.

In this article, we introduce an interesting topology-like concept concerning groups (and with almost the same method it can be defined for other algebraic systems). Given an arbitrary group $G$, we define a {\em topo-system} on $G$ as a…

We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties,…

We suggest a few projects for studying vertex algebras with emphasis on finite group viewpoints.

We apply compact group theory to obtain some model-theoretic results about the relativized Lascar Galois group of a strong type.

We survey some results on toric topology.

In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…

In this paper, we introduce the notion of F-manifold color algebras and study their properties which extend some results for F-manifold algebras.

The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…

This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

We classify the (filtered) Hopf actions of Hopf-Ore extensions of group algebras on path algebras of quivers, extending results in several other works from special cases to this general setting. Having done this for general Hopf-Ore…

We survey recent advances in non-abelian Hodge theory in the "mixed" setting of non-proper algebraic varieties. We then describe how these tools are used to construct algebraic Shafarevich morphisms and prove a version of the linear…