nLab Artin-Schelter regular algebra

Redirected from "Artin-Schelter regular ring".

Contents

Idea

A useful smoothness criterium for noncommutative graded algebras.

Definition

Let kk be a field and AA a connected finitely generated associative \mathbb{N} -graded kk-algebra.

AA is Artin-Schelter regular (AS regular) if the following three conditions hold:

  1. it is of finite global dimension dd

  2. has polynomial growth (dimA ndim A_n is bounded above by a polynomial function f(n)f(n))

  3. is Gorenstein: Ext A i( Ak,A)=0Ext_A^i({}_A k,A) = 0 for idi\neq d and Ext A d( Ak,A)=k AExt_A^d({}_A k,A) = k_A.

Literature

The notion was introduced (under the name regular algebra) in :

category: algebra

Last revised on June 25, 2024 at 17:41:37. See the history of this page for a list of all contributions to it.