Some Homological Properties of Skew PBW Extensions

Abstract

We prove that if R is a left Noetherian and left regular ring then the same is true for any bijective skew PBW extension A of R. From this we get Serre's Theorem for such extensions. We show that skew PBW extensions and its localizations include a wide variety of rings and algebras of interest for modern mathematical physics such as PBW extensions, well-known classes of Ore algebras, operator algebras, diffusion algebras, quantum algebras, quadratic algebras in 3-variables, skew quantum polynomials, among many others. We estimate the global, Krull and Goldie dimensions, and also Quillen's K-groups.

Key Words:

• Algebraic K-theory
• Global
• Graded rings
• Krull and goldie dimensions
• Noetherian regular noncommutative rings
• PBW extensions
• Quantum algebras
• Serre's theorem

2010 Mathematics Subject Classification:

• Primary 16S80, 16W25, 16S36, 16U20, 18F25
• Secondary 16W50, 16E65

ACKNOWLEDGMENTS

The authors are grateful to the editors and the referee for valuable suggestions and corrections.

Notes

Communicated by V. A. Artamonov.