Functorial, operadic and modular operadic combinatorics of circuit algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912238895366144 |
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| author | Raynor, Sophie |
| author_facet | Raynor, Sophie |
| contents | Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a dictionary for translating between their diverse incarnations and describing their wider context. A formal definition of a broad class of circuit algebras is established and three equivalent descriptions of circuit algebras are provided: in terms of operads of wiring diagrams, modular operads and categories of Brauer diagrams. As an application, circuit algebra characterisations of algebras over the orthogonal and symplectic groups are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20260 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functorial, operadic and modular operadic combinatorics of circuit algebras Raynor, Sophie Quantum Algebra Category Theory Representation Theory Circuit algebras are a symmetric analogue of Jones's planar algebras introduced to study finite-type invariants of virtual knotted objects. Circuit algebra structures appear, in different forms, across mathematics. This paper provides a dictionary for translating between their diverse incarnations and describing their wider context. A formal definition of a broad class of circuit algebras is established and three equivalent descriptions of circuit algebras are provided: in terms of operads of wiring diagrams, modular operads and categories of Brauer diagrams. As an application, circuit algebra characterisations of algebras over the orthogonal and symplectic groups are given. |
| title | Functorial, operadic and modular operadic combinatorics of circuit algebras |
| topic | Quantum Algebra Category Theory Representation Theory |
| url | https://arxiv.org/abs/2412.20260 |