Gendo-Frobenius algebras and comultiplication
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TL;DR
This paper introduces a new comultiplication for gendo-Frobenius algebras, generalizing known structures from Frobenius and gendo-symmetric algebras, and provides a novel characterization of gendo-Frobenius algebras.
Contribution
It constructs a unified comultiplication for gendo-Frobenius algebras and offers a new characterization that aids in understanding their structure.
Findings
Frobenius algebras are characterized by a compatible counit.
A new comultiplication for gendo-Frobenius algebras is constructed.
The paper unifies structures of Frobenius and gendo-symmetric algebras.
Abstract
Gendo-Frobenius algebras are a common generalisation of Frobenius algebras and of gendo-symmetric algebras. A comultiplication is constructed for gendo-Frobenius algebras, which specialises to the known comultiplications on Frobenius and on gendo-symmetric algebras. In addition, Frobenius algebras are shown to be precisely those gendo-Frobenius algebras that have a counit compatible with this comultiplication. Moreover, a new characterisation of gendo-Frobenius algebras is given. This new characterisation is a key for constructing the comultiplication of gendo-Frobenius algebras.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Topics in Algebra · Coding theory and cryptography