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  3. Coxeter Bialgebras
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  • Publisher:
    Cambridge University Press
    Publication date:
    October 2022
    November 2022
    ISBN:
    9781009243759
    9781009243773
    DOI:
    https://doi.org/10.1017/9781009243759
    Dimensions:
    (234 x 156 mm)
    Weight & Pages:
    1.59kg, 894 Pages
    Dimensions:
    Weight & Pages:
    • Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (186)
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    Subjects:
    Mathematics (general), Mathematics, Discrete Mathematics Information Theory and Coding, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (186)
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    Book description

    The goal of this monograph is to develop Hopf theory in the setting of a real reflection arrangement. The central notion is that of a Coxeter bialgebra which generalizes the classical notion of a connected graded Hopf algebra. The authors also introduce the more structured notion of a Coxeter bimonoid and connect the two notions via a family of functors called Fock functors. These generalize similar functors connecting Hopf monoids in the category of Joyal species and connected graded Hopf algebras. This monograph opens a new chapter in Coxeter theory as well as in Hopf theory, connecting the two. It also relates fruitfully to many other areas of mathematics such as discrete geometry, semigroup theory, associative algebras, algebraic Lie theory, operads, and category theory. It is carefully written, with effective use of tables, diagrams, pictures, and summaries. It will be of interest to students and researchers alike.

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    Contents

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    Contents

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