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arXiv · 1807.02491

Koszulity of finitely semi-graded algebras

José Oswaldo Lezama Serrano·Jaime Andrés Gómez Ortíz
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Abstract

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 Poincar\'e 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 Poincar\'e series.

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José Oswaldo Lezama Serrano, Jaime Andrés Gómez Ortíz. 2018-07-06. Koszulity of finitely semi-graded algebras. https://arxiv.org/abs/1807.02491

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