Ringel duality as an instance of Koszul duality

2017/01/22 by Bodzenta, Agnieszka, Külshammer, Julian · 1 citation
#14E05 #16G10 #18C20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1701.06222

Abstract

In their previous work, S. Koenig, S. Ovsienko and the second author showed that every quasi-hereditary algebra is Morita equivalent to the right algebra, i.e. the opposite algebra of the left dual, of a coring. Let A be an associative algebra and V an A-coring whose right algebra R is quasi-hereditary. In this paper, we give a combinatorial description of an associative algebra B and a B-coring W whose right algebra is the Ringel dual of R. We apply our results in small examples to obtain restrictions on the A_∞-structure of the \textrmExt-algebra of standard modules over a class of quasi-hereditary algebras related to birational morphisms of smooth surfaces.

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