Coxeter Bialgebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Coxeter Bialgebras write by Marcelo Aguiar. This book was released on 2022-10-31. Coxeter Bialgebras available in PDF, EPUB and Kindle. 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.
Bimonoids for Hyperplane Arrangements
Bimonoids for Hyperplane Arrangements - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bimonoids for Hyperplane Arrangements write by Marcelo Aguiar. This book was released on 2020-03-19. Bimonoids for Hyperplane Arrangements available in PDF, EPUB and Kindle. The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel-Hopf, Poincar -Birkhoff-Witt, and Cartier-Milnor-Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category theory.
Coxeter Groups and Hopf Algebras
Coxeter Groups and Hopf Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Coxeter Groups and Hopf Algebras write by Marcelo Aguiar. This book was released on 2006. Coxeter Groups and Hopf Algebras available in PDF, EPUB and Kindle. 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 constructing and 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 combinatorial objects which emerge naturally from the geometric viewpoint. This work lays a foundation and provides new insights for further development of the subject.
Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes)
Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) write by Heinrich G W Begehr. This book was released on 2003-08-04. Progress In Analysis, Proceedings Of The 3rd Isaac Congress (In 2 Volumes) available in PDF, EPUB and Kindle. The biannual ISAAC congresses provide information about recent progress in the whole area of analysis including applications and computation. This book constitutes the proceedings of the third meeting.
