Gendo-Frobenius algebras and comultiplication
Representation Theory
2021-07-30 v3 Rings and 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.
Keywords
Cite
@article{arxiv.2012.13758,
title = {Gendo-Frobenius algebras and comultiplication},
author = {Çiğdem Yırtıcı},
journal= {arXiv preprint arXiv:2012.13758},
year = {2021}
}
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14 pages