for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the...

A deformation U , of a graded K-algebra A is said to be of PBW type if grU is A. It has been shown for Koszul and N -Koszul algebras that the deformation is PBW if and only if the relations of U satisfy a Jacobi type condition. In particular, for these algebras the determination of the PBW property is a finite and explicitly determined linear algebra problem. We extend these results to an arbit...

let $alpha$ be an automorphism of a ring $r$. the authors [on skewinverse laurent-serieswise armendariz rings, comm. algebra 40(1)(2012) 138-156] applied the concept of armendariz rings to inverseskew laurent series rings and introduced skew inverselaurent-serieswise armendariz rings. in this article, we study on aspecial type of these rings and introduce strongly armendariz ringsof inverse ske...

We study the BGG Category O over a skew group ring, involving a finite group acting on a regular triangular algebra. We relate the representation theory of the algebra to Clifford theory for the skew group ring, and obtain results on block decomposition, semisimplicity, and enough projectives. O is also shown to be a highest weight category; the BGG Reciprocity formula is slightly different bec...

We study the BGG Category O over a skew group ring, involving a finite group acting on a regular triangular algebra. We relate the representation theory of the algebra to Clifford theory for the skew group ring, and obtain results on block decomposition, semisimplicity, and enough projectives. O is also shown to be a highest weight category; the BGG Reciprocity formula is slightly different bec...

This paper studies the structure of U(g)-Galois extensions. In particular, we use a result of Bell to construct a “PBW-like” free basis for faithfully flat U(g)-Galois extensions. We then move to non-faithfully flat extensions and propose a possible equivalent condition for a U(g)-extension to be Galois. We get a partial result for this.

We study the BGG Category O over a skew group ring, involving a finite group acting on a regular triangular algebra. We relate the representation theory of the algebra to Clifford theory for the skew group ring, and obtain results on block decomposition, semisimplicity, and enough projectives. O is also shown to be a highest weight category; the BGG Reciprocity formula is slightly different bec...