Enveloping Algebra and Skew Calabi-Yau algebras over Skew Poincar\'e-Birkhoff-Witt Extensions

TL;DR

This paper investigates the structure of skew PBW extensions, demonstrating that their tensor products are also skew PBW extensions, characterizing their enveloping algebras, and providing conditions for them to be skew Calabi-Yau algebras.

Contribution

It introduces new results on tensor products and enveloping algebras of skew PBW extensions, and establishes criteria for skew Calabi-Yau properties.

Findings

Tensor product of skew PBW extensions remains a skew PBW extension.

Characterization of the enveloping algebra of a skew PBW extension.

Sufficient conditions for skew PBW extensions to be skew Calabi-Yau algebras.

Abstract

In this paper we show that the tensor product of skew PBW extensions is a skew PBW ex- tension. We also characterize the enveloping algebra of a skew PBW extension. Finally, we establish sufficient conditions to guarantee the property of being skew Calabi-Yau algebra over skew PBW extensions.