arXiv subjects

José Oswaldo Lezama Serrano

Publications and source records attributed to José Oswaldo Lezama Serrano.

3 recordsLinked to original sources

arXiv2019

Koszulity of finitely semi-graded algebras

In this paper, we introduce the class of finitely semi-graded algebras which extends the connected graded algebras finitely generated in degree one. The Koszul behavior of finitely semi-graded algebras is investigated by the distributivity of some associated lattice of ideals. The Hilbert series, the Poincaré series and the Yoneda algebra are defined for this class of algebras. Finitely semi-graded algebras include many important examples of non $\mathbb{N}$-graded algebras finitely generated in degree one coming from mathematical physics, and for these concrete examples the Koszulity will be established, as well as, the explicit computation of its Hilbert and Poincaré series.

math.RA↗

arXiv2018

Center of skew PBW extensions

In this paper we compute the center of many noncommutative algebras that can be interpreted as skew $PBW$ extensions. We show that, under some natural assumptions on the parameters that define the extension, either the center is trivial, or, it is of polynomial type. As an application, we provided new examples of noncommutative algebras that are cancellative.

math.RA↗

arXiv2013

Automorphisms for skew PBW extensions and skew quantum polynomial rings

In this work we study the automorphisms of skew $PBW$ extensions and skew quantum polynomials. We use Artamonov's works as reference for getting the principal results about automorphisms for generic skew $PBW$ extensions and generic skew quantum polynomials. In general, if we have an endomorphism on a generic skew $PBW$ extension and there are some $x_i,x_j,x_u$ such that the endomorphism is not zero on this elements and the principal coefficients are invertible, then endomorphism act over $x_i$ as $a_ix_i$ for some $a_i$ in the ring of coefficients. Of course, this is valid for quantum polynomial rings, with $r=0$, as such Artamonov shows in his work. We use this result for giving some more general results for skew $PBW$ extensions, using filtred-graded techniques. Finally, we use localization for characterize some class the endomorphisms and automorphisms for skew $PBW$ extensions and skew quantum polynomials over Ore domains.

math.RA↗