Twin TQFTs and Frobenius Algebras
We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/407068 |
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| author | Carmen Caprau |
| author_facet | Carmen Caprau |
| author_sort | Carmen Caprau |
| collection | DOAJ |
| description | We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C,W,z,z∗) consists of a commutative Frobenius algebra C, a symmetric Frobenius algebra W, and an algebra homomorphism z:C→W with dual z∗:W→C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category. |
| format | Article |
| id | doaj-art-24ec3143514d4daea14f67b0ff180fec |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-24ec3143514d4daea14f67b0ff180fec2025-08-20T03:54:53ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/407068407068Twin TQFTs and Frobenius AlgebrasCarmen Caprau0Department of Mathematics, California State University, Fresno, 5245 North Backer Avenue M/S PB 108, Fresno, CA 93740-8001, USAWe introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C,W,z,z∗) consists of a commutative Frobenius algebra C, a symmetric Frobenius algebra W, and an algebra homomorphism z:C→W with dual z∗:W→C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category.http://dx.doi.org/10.1155/2013/407068 |
| spellingShingle | Carmen Caprau Twin TQFTs and Frobenius Algebras Journal of Mathematics |
| title | Twin TQFTs and Frobenius Algebras |
| title_full | Twin TQFTs and Frobenius Algebras |
| title_fullStr | Twin TQFTs and Frobenius Algebras |
| title_full_unstemmed | Twin TQFTs and Frobenius Algebras |
| title_short | Twin TQFTs and Frobenius Algebras |
| title_sort | twin tqfts and frobenius algebras |
| url | http://dx.doi.org/10.1155/2013/407068 |
| work_keys_str_mv | AT carmencaprau twintqftsandfrobeniusalgebras |