Noncommutative curves and noncommutative surfaces
JT Stafford, M Van den Bergh - Bulletin of the American Mathematical …, 2001 - ams.org
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 …
rings and, more generally, in the theory of abelian categories. Roughly speaking and by …
[HTML][HTML] Skew Calabi–Yau algebras and homological identities
M Reyes, D Rogalski, JJ Zhang - Advances in Mathematics, 2014 - Elsevier
A skew Calabi–Yau algebra is a generalization of a Calabi–Yau algebra which allows for a
non-trivial Nakayama automorphism. We prove three homological identities about the …
non-trivial Nakayama automorphism. We prove three homological identities about the …
Gorenstein subrings of invariants under Hopf algebra actions
E Kirkman, J Kuzmanovich, JJ Zhang - Journal of Algebra, 2009 - Elsevier
This paper concerns conditions on the action of a finite dimensional semisimple Hopf
algebra on an Artin–Schelter regular algebra that force the subring of invariants to satisfy the …
algebra on an Artin–Schelter regular algebra that force the subring of invariants to satisfy the …
[HTML][HTML] m-Koszul Artin–Schelter regular algebras
I Mori, SP Smith - Journal of Algebra, 2016 - Elsevier
This paper studies the homological determinants and Nakayama automorphisms of not-
necessarily-noetherian m-Koszul twisted Calabi–Yau or, equivalently, m-Koszul Artin …
necessarily-noetherian m-Koszul twisted Calabi–Yau or, equivalently, m-Koszul Artin …
Quantum binary polyhedral groups and their actions on quantum planes
We classify quantum analogues of actions of finite subgroups G of SL 2(k) on commutative
polynomial rings k[u, v]. More precisely, we produce a classification of pairs (H, R) where H …
polynomial rings k[u, v]. More precisely, we produce a classification of pairs (H, R) where H …
[HTML][HTML] Stable categories of graded maximal Cohen–Macaulay modules over noncommutative quotient singularities
I Mori, K Ueyama - Advances in Mathematics, 2016 - Elsevier
Tilting objects play a key role in the study of triangulated categories. A famous result due to
Iyama and Takahashi asserts that the stable categories of graded maximal Cohen …
Iyama and Takahashi asserts that the stable categories of graded maximal Cohen …
Graded maximal Cohen–Macaulay modules over noncommutative graded Gorenstein isolated singularities
K Ueyama - Journal of Algebra, 2013 - Elsevier
In this paper, we define a notion of noncommutative graded isolated singularity, and study
AS-Gorenstein isolated singularities and the categories of graded maximal Cohen …
AS-Gorenstein isolated singularities and the categories of graded maximal Cohen …
Noncommutative projective schemes and point schemes
I Mori - Algebras, rings and their representations, 2006 - World Scientific
Let k be a field and A be a noetherian graded algebra finitely generated in degree 1 over k.
There are two basic ingredients to study A in noncommutative algebraic geometry, namely …
There are two basic ingredients to study A in noncommutative algebraic geometry, namely …
Shephard–Todd–Chevalley theorem for skew polynomial rings
E Kirkman, J Kuzmanovich, JJ Zhang - Algebras and representation theory, 2010 - Springer
We prove the following generalization of the classical Shephard–Todd–Chevalley Theorem.
Let G be a finite group of graded algebra automorphisms of a skew polynomial ring …
Let G be a finite group of graded algebra automorphisms of a skew polynomial ring …