Orbifolding Frobenius Algebras

By R. Kaufmann. 2001

66 citations recorded by the source corpus.

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 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0b4b2d5ebe842537926a8491174e2ddd3098d675

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Johann Leida
2. A. Adem
3. Y. Ruan
4. G. Moore
5. G. Segal
6. Ashoke Sen
7. H. Iritani
8. Hsian-Hua Tseng

In Mathematical Physics

1. G. Moore
2. Johann Leida
3. A. Adem
4. Y. Ruan
5. G. Segal
6. H. Iritani
7. Hsian-Hua Tseng
8. Yunfeng Jiang

Citations in the corpus

• D-branes and K-theory in 2D topological field theory (2006, background): “In the context of 2D TFT two relevant references are [20][21].”
• Orbifolds and Stringy Topology (2007, methodology): “We work directly on g∈πorb 1 (X )Y g to simplify the notation [80], since for a πorb 1 (X )-effective suborbifold Z , the line bundle is always trivial.”