$S_3$-permuted Frobenius Algebras

Details $S_3$-permuted Frobenius Algebras $S_3$-permuted Frobenius Algebras

2011-03-26

arxiv.org/abs/1103.5113v1

Mathematics

Rings and Algebras

LaTeX, amspro, 13 pages; Proceedings of the 4th International Conference on Mathematical Sciences for Advancement of Science a

Scientific paper

In the present paper by Frobenius algebra Y we mean a finite dimensional algebra possessing an associative and invertible (nondegenerate) form a scalar product, referred to as the Frobenius structure. The nondegenerate form has an inverse. We drop the extra conditions of associativity and unitality of Y. Frobenius algebra is formulated within the monoidal abelian category of operad of graphs cat(m,n). Operad of graphs, i.e. diagrammatic language, is used both to illustrate the construction as well as a method of proof for the main Theorem. We give two detailed examples of this construction for Clifford algebras. Our construction, however, applies to all Frobenius algebras.

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