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Global Dimension 4 Extensions of Artin–Schelter Regular Algebras

✍ Scribed by Thomas Cassidy

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
210 KB
Volume
220
Category
Article
ISSN
0021-8693

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✦ Synopsis

Ž

.

x 106 1991 , pp. 335᎐388 and is either quadratic or cubic. The quadratic algebras A w are Koszul, and this fact was used by Le Bruyn, Smith, and Van den Bergh Le Ž .

x Bruyn et al., Math. Z. 222 1996 , 171᎐212 to classify the four-dimensional AS Ž . regular algebras D when is quadratic and deg z s 1. Alternative methods are Ž . needed when A is cubic or deg z ) 1. We prove in all such cases that the Ž . regularity of D and z is equivalent to the regularity of z in low degree e.g., 2 or 3 and this is equivalent to easily verifiable matrix conditions on the relations for D.

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