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, Poincaré–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.
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 Bialgebras
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.
Quasi-Hopf Algebras
Quasi-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 Quasi-Hopf Algebras write by Daniel Bulacu. This book was released on 2019-02-21. Quasi-Hopf Algebras available in PDF, EPUB and Kindle. This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
Basic Category Theory
Basic Category Theory - 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 Basic Category Theory write by Tom Leinster. This book was released on 2014-07-24. Basic Category Theory available in PDF, EPUB and Kindle. A short introduction ideal for students learning category theory for the first time.
