Handle element on nearly Frobenius algebras

TL;DR

This paper extends the concept of handle elements from Frobenius algebras to nearly Frobenius algebras, analyzing their properties, providing examples, and generalizing related concepts like Casimir and Schur elements.

Contribution

It introduces the handle element for nearly Frobenius algebras and explores its properties, expanding the understanding of algebraic structures related to Frobenius algebras.

Findings

Handle elements are extended to nearly Frobenius algebras.

Properties of handle elements are characterized and examples are provided.

Casimir and Schur elements are generalized for these algebra classes.

Abstract

In this article the concept of handle element of Frobenius algebras, as in [16], will be extended to nearly Frobenius algebras. The main properties of this element will be analyzed in this case and many examples will be constructed. Also the Casimir and Schur elements of symmetric algebras will be considered ([8]) and generalized for Frobenius and nearly Frobenius algebras showing which results still hold in this framework and which ones fail.