Volume: 14, Issue: 6 (2003)
pp. 573-617 DOI: 10.1142/S0129167X03001831
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Abstract |
Full Text (PDF, 445KB)
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| Title: |
Orbifolding Frobenius Algebras |
| Author(s): |
Ralph M. Kaufmann
Max-Planck Insitute for Mathematics,
Vivatsgasse 7, 53111 Bonn, Germany
Oklahoma State University,
Department of Mathematics, 401 MS, Stillwater,
OK 74078, USA
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| History: |
Received 28 October 2002
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| Abstract: |
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. |
| Keywords: |
Global quotients; orbifolds; stringy cohomology; finite gauge (topological field) theory
AMSC numbers:
14F43, 14N32, 58D29, 81E40
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