Nearly Frobenius dimension of Frobenius algebras

Abstract

This article is divided into two parts. In the first part we work over a field $\mathbb{k}$ and prove that the Frobenius space associated to a Frobenius algebra is generated as left A-module by the Frobenius coproduct. In particular, we prove that the Frobenius dimension coincides with the dimension of the algebra. In the second part we work with a commutative ring k and prove that the Frobenius space associated to a Frobenius algebra is generated as left A-module by the Frobenius coproduct. We introduce the concept of nearly Frobenius algebras in this context and construct solutions of the quantum Yang-Baxter equation starting from elements in the Frobenius space. Also, we give an alternative characterization of a nearly Frobenius algebra.

Keywords:

• Frobenius algebras
• Frobenius dimension
• nearly Frobenius algebras
• Quantum Yang-Baxter equation

2020 Mathematics Subject Classification:

• 16W99
• 16D99
• 16T25