2022/04/29 by Amanda Hernandez, Hernandez, Amanda, Chelsea Walton +3 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2204.14182
A Frobenius algebra is a finite-dimensional algebra A which comes equipped with a coassociative, counital comultiplication map Δ 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 Δ as above that is not necessarily counital. We also conjecture that this comultiplicative structure holds for self-injective algebras in general.