2024/02/05 by Shimizu, Kenichi
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2402.02929
We introduce the notion of a quasi-Frobenius algebra in a finite tensor category C and give equivalent conditions for an algebra in C to be quasi-Frobenius. A quasi-Frobenius algebra in C is not necessarily Frobenius, however, we show that an algebra A in C is quasi-Frobenius if and only if A is Morita equivalent to a Frobenius algebra in C. We also show that the class of symmetric Frobenius algebras in C is closed under the Morita equivalence provided that C is pivotal so that the symmetricity makes sense.