Regularity and K0-group of quadric solvable polynomial algebras

Abstract

Concerning solvable polynomial algebras in the sense of Kandri-Rody and Weispfenning [J. Symbolic Comput. 9 (1990) 1–26], it is shown how to recognize and construct quadric solvable polynomial algebras in an algorithmic way. If A= k[ a 1,…, a n ] is a quadric solvable polynomial algebra, it is proved that gl.dim A⩽ n and K 0(A)≅ Z . If A is a tame quadric solvable polynomial algebra, it is shown that A is completely constructable and Auslander regular.