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Regularity of modules over a Koszul algebra

✍ Scribed by Luchezar L Avramov; David Eisenbud


Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
271 KB
Volume
153
Category
Article
ISSN
0021-8693

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We prove the simple fact that the factor ring of a Koszul algebra by a regular, normal, quadratic element is a Koszul algebra. This fact leads to a new construction of quadratic Artin᎐Schelter regular algebras. This construction generalizes the construction of Artin᎐Schelter regular Clifford algebra

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Let A be a three dimensional Artin᎐Schelter regular algebra. We give a description of the category of finitely generated A-modules of Gelfand᎐Kirillov Ž . dimension one modulo those of finite dimension over the ground field . The proof is based upon a result by Gabriel which says that locally finite