A bocs theoretic characterization of gendo-symmetric algebras

作者：Marczinzik Rene^*

来源：Journal of Algebra, 2017, 470: 160-171.

DOI：10.1016/j.jalgebra.2016.08.041

• Representation theory of finite
• dimensional algebras
• Corings
• Dominant dimension

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.

• 出版日期2017-1-15