The Gabriel Quiver Of Several Classes Of Finite EI Categories Of Alternating Groups A₄

Representation theory of EI categories,which are small categories such that every endomorphism is an isomorphism,is closely related to representation theory of groups.On one hand,it is an important extension of group representation theory;on the other hand,we can construct many EI categories from a given group such as transporter category,orbit category,Forbenius category,and fusion systems,which play a fundamental role in representation theory and cohomology theory of groups.In this paper we describe the structures of transporter category,orbit category and Forbenius category for the alternating group A4,and construct the Gabriel quivers of the category algebras over the complex field for these categories.