2021/09/08 by Külshammer, Julian, Miemietz, Vanessa
#16E45 #16G10 (Primary) #18C20 #18G55 (Secondary) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2109.03586
Together with Koenig and Ovsienko, the first author showed that every quasi-hereditary algebra can be obtained as the (left or right) dual of a directed bocs. In this monograph, we prove that if one additionally assumes that the bocs is basic, a notion we define, then this bocs is unique up to isomorphism. This should be seen as a generalisation of the statement that the basic algebra of an arbitrary associative algebra is unique up to isomorphism. The proof associates to a given presentation of the bocs an A_∞-structure on the Ext-algebra of the standard modules of the corresponding quasi-hereditary algebra. Uniqueness then follows from an application of Kadeishvili's theorem.