Coxeter Groups and Hopf Algebras

An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructingand studying many of these objects as well as new ones. The first three chapters introduce the necessary background ideas making this work accessible to advanced graduate students. The later chapters culminate in a unified and conceptual construction of several Hopf algebras based on combinatorialobjects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject. To read more about Coxeter groups see The Coxeter Legacy: Reflections and Projections. Information for our distributors: Titles in this series are copublished with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).Aguiar, Marcelo is the author of 'Coxeter Groups and Hopf Algebras ', published 0006 under ISBN 9780821839072 and ISBN 0821839071.