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- W2101472429 abstract "This paper revolves around two main results. First, we propose a hom-set type categorification of virtual braid groups and positive virtual braid monoids in terms of locally braided objects in a symmetric category (SC). This double braiding approach provides a rich source of representations, and offers a natural categorical interpretation for virtual racks and for the twisted Burau representation. Second, we define self-distributive (SD) structures in an arbitrary SC. SD structures are shown to produce braided objects in a SC. As for examples, we interpret the associativity and the Jacobi identity in a SC as generalized self-distributivity, thus endowing associative and Leibniz algebras with a (pre-)braiding. A homology theory of categorical SD structures is developed using the braided techniques from [Lebed, Homologies of algebraic structures via braidings and quantum shuffles, to appear in J. Algebra], generalizing rack, bar, Leibniz and other familiar complexes." @default.
- W2101472429 created "2016-06-24" @default.
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- W2101472429 date "2013-08-01" @default.
- W2101472429 modified "2023-10-01" @default.
- W2101472429 title "CATEGORICAL ASPECTS OF VIRTUALITY AND SELF-DISTRIBUTIVITY" @default.
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- W2101472429 doi "https://doi.org/10.1142/s0218216513500454" @default.
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