Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras of type S

2024/08/05 by Liu, Yuming, Xing, Bohan
#16G10 #16G20 #16S99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2408.02537

Abstract

By giving some equivalent definitions of fractional Brauer configuration algebras of type S in some special cases, we construct a fractional Brauer configuration algebra from any monomial algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Moreover, we show that there exists a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with trivial degree function and a given admissible cut over it.

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