Spheres as Frobenius objects
Following the pattern of the Frobenius structure usually assigned to the 1-dimensional sphere, we investigate the Frobenius structures of spheres in all other dimensions. Starting from dimension d=1, all the spheres are commutative Frobenius objects in categories whose arrows are (d+1)-dimensional c...
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| Veröffentlicht in: | Theory and applications of categories 2018-01, Vol.33 (42), p.691 |
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| creator | Baralic, Djordje Petric, Zoran Telebakovic, Sonja |
| description | Following the pattern of the Frobenius structure usually assigned to the 1-dimensional sphere, we investigate the Frobenius structures of spheres in all other dimensions. Starting from dimension d=1, all the spheres are commutative Frobenius objects in categories whose arrows are (d+1)-dimensional cobordisms. With respect to the language of Frobenius objects, there is no distinction between these spheres - they are all free of additional equations formulated in this language. The corresponding structure makes out of the 0-dimensional sphere not a commutative but a symmetric Frobenius object. This sphere is mapped to a matrix Frobenius algebra by a 1-dimensional topological quantum field theory, which corresponds to the representation of a class of diagrammatic algebras given by Richard Brauer. |
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Starting from dimension d=1, all the spheres are commutative Frobenius objects in categories whose arrows are (d+1)-dimensional cobordisms. With respect to the language of Frobenius objects, there is no distinction between these spheres - they are all free of additional equations formulated in this language. The corresponding structure makes out of the 0-dimensional sphere not a commutative but a symmetric Frobenius object. This sphere is mapped to a matrix Frobenius algebra by a 1-dimensional topological quantum field theory, which corresponds to the representation of a class of diagrammatic algebras given by Richard Brauer.</description><identifier>EISSN: 1201-561X</identifier><language>eng</language><publisher>Sackville: R. 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| ispartof | Theory and applications of categories, 2018-01, Vol.33 (42), p.691 |
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| subjects | Algebra Dimensional analysis Field theory Mathematical analysis Mathematics Matrix methods Quantum field theory Quantum theory Spheres |
| title | Spheres as Frobenius objects |
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