A bocs theoretic characterization of gendo-symmetric algebras

JOURNAL OF ALGEBRA

卷:470

Article

Marczinzik, Rene¹ 

[1] Univ Stuttgart, Inst Algebra & Theory, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Representation theory of finite;    dimensional algebras;    Corings;    Dominant dimension;   

DOI  :  10.1016/j.jalgebra.2016.08.041

来源: Elsevier

【 摘 要 】

Gendo-symmetric algebras were recently introduced by Fang and Konig in [7]. 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 equivalent 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free