2011/03/26 by Zbigniew Oziewicz, Oziewicz, Zbigniew, G. P. Wene +2 · 1 citation
Engineering · Mathematics · #05A15 #05C38 #15A15 #15A18 #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.CT #math.RA #msc:05A15 #msc:05C38 #msc:15A15 #msc:15A18
paper · pdf · doi:10.48550/arxiv.1103.5113
LaTeX, amspro, 13 pages; Proceedings of the 4th International Conference on Mathematical Sciences for Advancement of Science and Technology, Kolkata (Calcutta), India, December 2010. Institute for Mathematics, Bio-informatics, Information-technology and Computer-science, IMBIC, http://www.imbic.org/index.html
arxiv created 2011/03/26 · openalex publication_date 2011/03/26 · arxiv updated 2011/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.