In this survey article we describe some geometric results in the theory of noncommutative
rings and, more generally, in the theory of abelian categories. Roughly speaking and by …

The aim of this paper is to develop the theory of Hom-coalgebras and related structures.
After reviewing some key constructions and examples of quasi-deformations of Lie algebras …

This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

There are two aspects to this survey. First, in Sections 1-3 we give an introduction to the
main ideas and fundamental results in the theory of Artin-Schelter regular algebras, suitable …

Quasi-Lie algebras Page 256 http://dx. doi. org/10.1090/conm/391/07333 Contemporary
Mathematics Volume 391, 2005 Quasi-Lie algebras Daniel Larsson and Sergei D. Silvestrov …

In this article we apply a method devised in Hartwig, Larsson, and Silvestrov and Larsson
and Silvestrov to the simple 3-dimensional Lie algebra 𝔰𝔩2 (𝔽). One of the main points of …

Page 1 MEMOIRS Of the American Mathematical Society Number 734 Blowing Up of Non-Commutative
Smooth Surfaces Michel Van den Bergh November 2001 • Volume 154 • Number 734 (end of …

We study two classes of quadratic algebras over a field k: the class Cn of all n-generated
PBW algebras with polynomial growth and finite global dimension, and the class of quantum …

We construct four families of Artin-Schelter (AS) regular algebras of global dimension 4. This
is a complete list of AS regular algebras of global dimension 4 which are generated by two …

A double Ore extension is a natural generalization of the Ore extension. We prove that a
connected graded double Ore extension of an Artin–Schelter regular algebra is Artin …