Returning Arrows for Self-injective Algebras and Artin-Schelter Regular Algebras

Details Returning Arrows for Self-injective Algebras and Artin-Schelter Regular Algebras Returning Arrows for Self-injective Algebras and Artin-Schelter Regular Algebras

2010-12-22

arxiv.org/abs/1012.4864v2

Mathematics

Rings and Algebras

The title is changed. The results on the self-injective algebras are improved, and their dual versions for Koszul Artin-Schelt

Scientific paper

In this paper, we discuss returning arrows with respect to the Nakayama translation appearing in the quivers of some important algebras when we construct extensions. When constructing twisted trivial extensions for a graded self-injective algebra, we show that the returning arrows appear in the quiver, that the complexity increases by 1 in Koszul cases, and the representation dimension also increases by 1 under certain additional conditions. By applying Koszul duality, for each Koszul Artin-Schelter regular algebra of global dimension l and Gelfand-Kirilov dimension $c$, we construct a family of Koszul Artin-Schelter regular algebras of global dimension $l+1$ and Gelfand-Kirilov dimension $c+1$, among them one is central extension and one is $l+1$-Calabi-Yau.

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