We study the general theory of Frobenius algebras with group actions. These structures arise when one is studying the algebraic structures associated to a geometry stemming from a physical theory with a global finite gauge group, i.e. orbifold theories. In this context, we introduce and axiomatize these algebras. Furthermore, we define a geometric cobordism categories whose functors to the category of vector spaces are parameterized by these algebras. The theory is also extended to the graded and super-graded cases. As an application, we consider Frobenius algebras having some additional properties making them more tractable. These properties are present in Frobenius algebras arising as quotients of Jacobian ideal, such as those having their origin in quasi-homogeneous singularities and their symmetries.
arXiv Mathematics e-prints
- Pub Date:
- July 2001
- Mathematics - Algebraic Geometry
- 42 pages LaTex. Paper version of talks at WAGP2000 in Oct 2000 and at``Mathematical apspects of orbifold string theoy'' in May 2001 Revised version: Typos corrected, slight revisions in the last section