Talk:Frobenius algebra

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Mathematics rating:	Start Class	Low Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. This is just about no longer a stub, but needs lots more expansion and work, plus some references. Geometry guy 21:10, 21 May 2007 (UTC)

I expanded the article a bit and gave a good reference for history and algebraic study of Frobenius algebras. In particular, everything up to the categorical stuff is easily found in Lam (which has several sections on Frobenius algebras), and everything after is unsourced, but I remember some Baez article about this.

I did not actually include the duality theory which plays a prominent role in the study of Quasi-Frobenius rings and Iwanaga-Gorenstein rings. In particular, I did not include the classical contributions of Nakayama (because he has no wiki bio!) on the Nakayama permutation, the relations amongst the simple modules, and socle/head duality. Nor did I include Nakayama's term for these algebras, Frobeniusean, since he is the only one who used it more than once. Similarly, symmetric algebras received almost no special treatment, even though they are a fundamentally important special case. The generalizations to Frobenius rings, Quasi-Frobenius rings, and self-injective rings are not included here, but perhaps this would be a good place if quasi-frobenius does not get its own article. Lam would provide a good reference for the intuitive differences between these notions, but for generalizations of QF, one needs to look elsewhere (Faith's Rings and Things for instance has quite a few such generalizations). JackSchmidt (talk) 09:19, 23 November 2007 (UTC)

Lam also acts as a source for the TQFT remarks, but has nothing on the categorical definition. I included a few other remarks too. JackSchmidt (talk) 09:55, 23 November 2007 (UTC)