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[a1,..., an] is a quadric solvable polynomial algebra, it is proved that gl.dim A ≤ n and K0(A) ≅ ℤ. If A is a tame quadric solvable polynomial algebra, it is shown that A is completely constructable and Auslander regular.