A bocs theoretic characterization of gendo-symmetric algebras

2016/06/23 by Marczinzik, Rene · 1 citation
#16E10 #16G10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1606.07272

Abstract

Gendo-symmetric algebras were recently introduced by Fang and König. An algebra is called gendo-symmetric in case it is isomorphic to the endomorphism ring of a generator over a finite dimensional symmetric algebra. We show that a finite dimensional algebra A over a field K is gendo-symmetric if and only if there is a bocs-structure on (A,D(A)), where D=Hom_K(-,K) is the natural duality. Assuming that A is gendo-symmetric, we show that the module category of the bocs (A,D(A)) is isomorphic to the module category of the algebra eAe, when e is an idempotent such that eA is the unique minimal faithful projective-injective right A-module. We also prove some new results about gendo-symmetric algebras using the theory of bocses.

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