arXiv subjects
Publications and source records attributed to Karol Herrera.
We investigate the annihilator condition $(a.c.)$ for skew Poincaré-Birkhoff-Witt extensions. We prove that some results about the annihilator condition $(a.c.)$ for skew polynomial rings also hold for skew PBW extensions. We also demonstrate that the behavior of annihilators is determined by the defining relations of the extension. Our results extend those corresponding presented for skew polynomial rings
In this paper, we compute the Gröbner-Shirshov bases for certain regular double extension algebras by means of an algorithm implemented in Matlab, which facilitates the underlying algebraic computations. Moreover, we establish that these families also admit a PBW basis.
We study the differential smoothness of Sklyanin algebras in three and four variables. We show that all non-degenerate three-dimensional cases are differentially smooth, while none of the four-dimensional Sklyanin algebras admit a connected integrable differential calculus of suitable dimension.