Second quantized Frobenius algebras. (Q1885606)

This paper is a continuation of [Int. J. Math. 14, No. 6, 573-617 (2003; Zbl 1083.57037)]. In that paper, the author introduced the notion of \(G\)-Frobenius algebras together with graded and super versions, where \(G\) is a finite group. The motivation was an equivariant version of 1+1 dimensional topological field theory. In the present paper, the author reviews the notions and results from his previous article. Then ``Intersection'' and Jacobian \(G\)-Frobenius algebras are studied in detail. Special \(G\)-Frobenius algebras -- those with \(\dim A_g=1\) for all \(g\in G\) -- were described in the previous paper in terms of 2-cocycles, generalizing the well-known description of strongly graded algebras. A concrete presentation is given here for \(G={\mathbf S}_n\). The last section is devoted to ``second quantized Frobenius algebras'', again here \(G={\mathbf S}_n\).