Two-dimensional topological quantum field theories and Frobenius algebras

被引：99

作者：

Abrams, L

机构：

[1] Johns Hopkins University, Department of Mathematics, Baltimore, MD 21218

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 1996年 / 5卷 / 05期

关键词：

topological quantum field theory; frobenius algebra; two-dimensional cobordism; category theory;

D O I：

10.1142/S0218216596000333

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. This characterization allows a simple demonstration of the compatibility of Frobenius algebra structure with direct sums. We then classify the indecomposable Frobenius algebras as being either ''annihilator algebras'' algebras whose socle is a principal ideal - or field extensions. The relationship between two-dimensional topological quantum field theories and Frobenius algebras is then formulated as an equivalence of categories. The proof hinges on our new characterization of Frobenius algebras. These results together provide a classification of the indecomposable two-dimensional topological quantum field theories.

引用

页码：569 / 587

页数：19

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