Categories and Weak Equivalences of Graded Algebras

Categories and Weak Equivalences of Graded

Algebras

Alexey Gordienko; Ofir Schnabel; James Zhang

【期刊名称】《代数集刊：英文版》 【年(卷),期】2019(026)004

【摘要】In the study of the structure of graded algebras(such as graded ideals,graded

subspaces,and

radicals)or

graded

polynomial

identities,the grading group can be replaced by any other group that realizes the same grading.Here we come to the notion of weak equivalence of gradings:two gradings are weakly equivalent if there exists an isomorphism between the graded algebras that maps each graded component onto a graded component.Each group grading on an algebra can be weakly equivalent to G-gradings for many different groups G;however,it turns out that there is one distinguished group among them,called the universal group of the grading.In this paper we study categories and functors related to the notion of weak equivalence of gradings.In particular,we introduce an oplax 2-functor that assigns to each grading its support,and show that the universal grading group functor has neither left nor right adjoint. 【总页数】22页(P.643-664)

【关键词】algebra; grading; adjoint functor; oplax 2-functor; (co)limit 【作者】Alexey Gordienko; Ofir Schnabel; James Zhang