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Coxeter Bialgebras (Hardcover)
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Coxeter Bialgebras (Hardcover)
Series: Encyclopedia of Mathematics and its Applications
Expected to ship within 12 - 17 working days
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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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