Quantum groups and noncommutative geometry. With a contribution by Theo Raedschelders and Michel Van den Bergh

DOI10.1007/978-3-319-97987-8zbMath1430.16001OpenAlexW2896780279MaRDI QIDQ1668471

Yuri I. Manin

Publication date: 28 August 2018

Published in: CRM Short Courses (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-97987-8

zbMATH Keywords

quantum groupYang-Baxter equationtensor categorycompact matrix pseudogroupquadratic Hopf algebraquantum matrix space

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Noncommutative geometry in quantum theory (81R60) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) Ring-theoretic aspects of quantum groups (16T20) Bialgebras (16T10) Research exposition (monographs, survey articles) pertaining to group theory (20-02) Hopf algebras and their applications (16T05) Yang-Baxter equations (16T25) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

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Symmetric ordering and Weyl realizations for quantum Minkowski spaces ⋮ Quantum groups and polymer quantum mechanics ⋮ Composing PROBs ⋮ Right-covariant differential calculus on Hopf superalgebra \(\mathbb{F}(\mathbb{C}_q^{2|1})\) ⋮ Hecke symmetries: an overview of Frobenius properties ⋮ Resolutions for twisted tensor products ⋮ Determinants in quantum matrix algebras and integrable systems ⋮ Non-Archimedean quantum mechanics via quantum groups ⋮ Frobenius-Perron theory of representations of quivers

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