A Note on Solvable Polynomial Algebras

Abstract

In terms of their defining relations, solvable polynomial algebras introduced by Kandri-Rody and Weispfenning [J. Symbolic Comput., 9(1990)] are characterized by employing Gr\"obner bases of ideals in free algebras, thereby solvable polynomial algebras are completely determinable and constructible in a computational way.

Keywords

• PBW basis
• Monomial ordering
• Gr\"obner basis
• Solvable polynomial algebra