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

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.