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.

[1]  H. Su'arez,et al.  PBW bases for some 3-dimensional skew polynomial algebras , 2017, 1805.03489.

[2]  H. Su'arez,et al.  A generalized Koszul property for skew PBW extensions , 2017, 1804.06615.

[3]  A. Reyes,et al.  Armendariz property for skew PBW extensions and their classical ring of quotients , 2016 .

[4]  Milton Armando Reyes Villamil,et al.  Some Remarks About the Cyclic Homology of Skew PBW Extensions / Algunas observaciones sobre la homología cíclica de extensiones PBW torcidas , 2016 .

[5]  H. Su'arez,et al.  Koszulity for skew PBW extensions over fields , 2016, 1611.04483.

[6]  H. Suárez.  Koszulity for graded skew PBW extensions , 2016, 1610.04275.

[7]  A. Reyes,et al.  A note on zip and reversible skew PBW extensions , 2016 .

[8]  A. Reyes.  Skew PBW Extensions of Baer, quasi-Baer, p.p. and p.q.-rings , 2015 .

[9]  H. Suáreza,et al.  Some Relations between N-Koszul , Artin-Schelter Regular and Calabi-Yau Algebras with Skew PBW Extensions , 2015 .

[10]  A. Reyes.  Jacobson's conjecture and skew PBW extensions , 2014 .

[11]  A. Reyes.  Uniform Dimension over Skew PBW Extensions , 2014 .

[12]  O. Lezama,et al.  Prime ideals of skew PBW extensions , 2014, 1402.2321.

[13]  C. Zhu,et al.  Nakayama automorphisms of double Ore extensions of Koszul regular algebras , 2014, 1401.0330.

[14]  Manuel Reyes,et al.  Skew Calabi–Yau algebras and homological identities , 2013, 1302.0437.

[15]  O. Lezama,et al.  Some Homological Properties of Skew PBW Extensions , 2013, 1310.6639.

[16]  A. Reyes.  Gelfand-Kirillov Dimension of Skew PBW Extensions , 2013 .

[17]  L.-Y. Liu,et al.  Twisted Calabi-Yau property of Ore extensions , 2012, 1205.0893.

[18]  Q.-S. Wu,et al.  Skew group algebras of Calabi–Yau algebras , 2011 .

[19]  O. Lezama,et al.  Gröbner Bases for Ideals of σ-PBW Extensions , 2010 .

[20]  Louis Rowen,et al.  Graduate Algebra: Commutative View , 2006 .

[21]  C. Weibel,et al.  An Introduction to Homological Algebra: References , 1960 .