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arXiv · 2204.14182

On non-counital Frobenius algebras

Amanda Hernandez·Chelsea Walton·Harshit Yadav
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Abstract

A Frobenius algebra is a finite-dimensional algebra $A$ which comes equipped with a coassociative, counital comultiplication map $\Delta$ that is an $A$-bimodule map. Here, we examine comultiplication maps for generalizations of Frobenius algebras: finite-dimensional self-injective (quasi-Frobenius) algebras. We show that large classes of such algebras, including finite-dimensional weak Hopf algebras, come equipped with a nonzero map $\Delta$ as above that is not necessarily counital. We also conjecture that this comultiplicative structure holds for self-injective algebras in general.

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Amanda Hernandez, Chelsea Walton, Harshit Yadav. 2022-04-29. On non-counital Frobenius algebras. https://arxiv.org/abs/2204.14182

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