Polyadic Hopf algebras

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ID: 311721
2022
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Abstract
In chapter 9 generalized polyadic coassociative coalgebras, bialgebras and Hopf algebras are defined and investigated. They have many unusual features in comparison with the binary case. For instance, both the algebra and its underlying field can be zeroless and nonunital, the existence of the unit and counit is not obligatory, while the dimension of the algebra is not arbitrary, but ‘quantized’. The polyadic convolution product and bialgebra can be defined, and when the algebra and coalgebra have unequal arities, the polyadic version of the antipode, the querantipode, has different properties. We introduce the polyadic version of braidings, almost co-commutativity, quasitriangularity and the equations for the R-matrix (which can be treated as a polyadic analog of the Yang–Baxter equation). We propose another concept of deformation which is governed not by the twist map, but by the medial map. We present the corresponding braidings, almost co-mediality and M-matrix (the medial analog of the R-matrix), for which compatibility equations are found.
Reference Key
persistent_1771691439_6999ddafb1ea0 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Steven Duplij
Journal science and technology of advanced materials
Year 2022
DOI
10.1088/978-0-7503-2648-3ch9
URL
https://iopscience.iop.org/book/mono/978-0-7503-2648-3/chapter/bk978-0-7503-2648-3ch9.pdf
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