Second quantized Frobenius algebras

Details Second quantized Frobenius algebras Second quantized Frobenius algebras

2002-06-13

arxiv.org/abs/math/0206137v3

Commun.Math.Phys. 248 (2004) 33-83

Mathematics

Algebraic Geometry

39p. Latex. New version fixes sign mistake and includes the full description of discrete torsion

Scientific paper

10.1007/s00220-004-1090-y

We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n--th tensor powers, where the quotients are given by symmetric group twisted Frobenius algebras. To this end, we consider the setting of Frobenius algebras given by functors from geometric categories whose objects are endowed with geometric group actions and prove structural results, which in turn yield a constructive realization in the case of n--th tensor powers and the natural permutation action. We also show that naturally graded symmetric group twisted Frobenius algebras have a unique algebra structure already determined by their underlying additive data together with a choice of super--grading. Furthermore we discuss several notions of discrete torsion andshow that indeed a non--trivial discrete torsion leads to a non--trivial super structure on the second quantization.

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