Raynor, Sophie (2025) Functorial, operadic and modular operadic combinatorics of circuit algebras. Journal of Pure and Applied Algebra, 229 (11). 108105.

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Abstract

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.

Item ID:	89346
Item Type:	Article (Research - C1)
ISSN:	1873-1376
Copyright Information:	© 2025 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Funders:	Australian Research Council (ARC)
Projects and Grants:	ARC DP160101519, ARC FT160100393
Date Deposited:	28 Oct 2025 00:59
FoR Codes:	49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490401 Algebra and number theory @ 100%
SEO Codes:	28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 100%
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