Titlebook: Quantum Groups and Noncommutative Geometry; Yuri I. Manin Textbook 2018Latest edition Springer Nature Switzerland AG 2018 quantum groups.H

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Theo Raedschelders,Michel Van den Berghds of East African origin. In so doing, China commenced its own tradition of exchange with East Africa—one that was conducted on a somewhat lower but nonetheless comparable scale with the preexistent and more direct trade pursued by merchants hailing from the various contemporary countries of the Ar

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https://doi.org/10.1007/978-3-319-97987-8quantum groups; Hopf algebras; Tanaka-Krein; coalgebras; bialgebras; monoidal categories; noncommutative g

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Quantum Groups and Noncommutative Geometry978-3-319-97987-8Series ISSN 2522-5200 Series E-ISSN 2522-5219

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The Quantum Group ,e to imagine the ring . as a ring of (polynomial) functions on a space which is an object of noncommutative, or “quantum,” geometry. Morphisms of spaces correspond to ring homomorphisms in the opposite direction. For . and . fixed, the set . is also called the set of .-. defined by ..

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Frobenius Algebras and the Quantum Determinant,e where this pairing is nonsymmetric for ., see [30]. This asymmetry is the reason why the quantum determinant considered in Example . might be noncentral.) The algebra . is called a . if, in addition, (c) ..

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,Yang–Baxter Equations, the following prescription: represent each element . as a product of transpositions of neighbors and apply . instead of each .. Of course, such a decomposition is nonunique but the resulting linear operator does not depend on it.

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,The Tannaka–Krein Formalism and (Re)Presentations of Universal Quantum Groups,recisely, our goal is to convince the reader that, as long as one starts with a reasonable algebra ., the universal bi- and Hopf algebras . and . introduced in Chapters . and . are well-behaved objects.