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Coxeter Bialgebras by Marcelo Aguiar

Coxeter Bialgebras

by Marcelo Aguiar
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Book cover type: Hardcover
  • ISBN13: 9781009243773
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: N/A
  • Original Price: USD 189.0
  • Language: English
  • Edition: N/A
  • Item Weight: 1565 grams
  • BISAC Subject(s): Algebra / General and Algebra / Linear

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.

Aguiar, Marcelo: - Marcelo Aguiar is Professor in the Department of Mathematics at Cornell University, Ithaca.

Mahajan, Swapneel: - Swapneel Mahajan is Associate Professor in the Department of Mathematics at the Indian Institute of Technology, Mumbai.

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