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arXiv · 2408.02537

Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras

Yuming Liu·Bohan Xing
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Abstract

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish 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 a free fractional-degree function and an admissible cut on it.

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Yuming Liu, Bohan Xing. 2024-08-05. Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras. https://doi.org/10.1007/s10468-026-10378-5

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