Titlebook: A Course on Hopf Algebras; Rinat Kashaev Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springe

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Agatha Christie: Power and IllusionThe main goal of this chapter is

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Agatha Christie: Power and IllusionOur main goal in this chapter is to show that Hopf algebras are abundant, and that there exist general methods of producing examples. We start by describing constructions of algebras which are common and well known. Then, we proceed with less well known constructions of coalgebras, bialgebras and Hopf algebras.

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https://doi.org/10.1057/9780230598270Let . be a Hopf algebra. In this chapter, we work out the structure of the Hopf algebra . in few simple examples. The fact that . a Hopf algebra (instead of being just a coalgebra) often facilitates its description.

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Agatha Christie, Poison, and Crime,In this chapter, we present certain aspects of quantum invariants of knots and links.

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https://doi.org/10.1007/978-3-031-16000-4icians, (Berkeley, CA, 1986), vol. 1, 2, pp. 798–820. American Mathematical Society, Providence, 1987). It allows to associate to any Hopf algebra with invertible antipode another Hopf algebra whose category of finite-dimensional representations is canonically braided. In this chapter, following Kas

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Rinat KashaevIncludes advanced applications to knot theory, such as the construction of solutions to Yang–Baxter equations.Uses string diagrams to facilitate understanding.Assumes only minimal background for most

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A Course on Hopf Algebras978-3-031-26306-4Series ISSN 0172-5939 Series E-ISSN 2191-6675

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Textbook 2023s of the Yang–Baxter equations..Starting with a reformulation of the definition of a group in terms of structural maps as motivation for the definition of a Hopf algebra, the book introduces the related algebraic notions: algebras, coalgebras, bialgebras, convolution algebras, modules, comodules. Ne