Hopf Algebras and Their Actions on Rings - 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 Hopf Algebras and Their Actions on Rings write by Susan Montgomery. This book was released on 1993-10-28. Hopf Algebras and Their Actions on Rings available in PDF, EPUB and Kindle. The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.
Classical Hopf Algebras and Their Applications
Classical Hopf Algebras and Their Applications - 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 Classical Hopf Algebras and Their Applications write by Pierre Cartier. This book was released on 2021-09-20. Classical Hopf Algebras and Their Applications available in PDF, EPUB and Kindle. This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras.
Hopf Algebras and Root Systems
Hopf Algebras and Root Systems - 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 Hopf Algebras and Root Systems write by István Heckenberger. This book was released on 2020-06-19. Hopf Algebras and Root Systems available in PDF, EPUB and Kindle. This book is an introduction to Hopf algebras in braided monoidal categories with applications to Hopf algebras in the usual sense. The main goal of the book is to present from scratch and with complete proofs the theory of Nichols algebras (or quantum symmetric algebras) and the surprising relationship between Nichols algebras and generalized root systems. In general, Nichols algebras are not classified by Cartan graphs and their root systems. However, extending partial results in the literature, the authors were able to associate a Cartan graph to a large class of Nichols algebras. This allows them to determine the structure of right coideal subalgebras of Nichols systems which generalize Nichols algebras. As applications of these results, the book contains a classification of right coideal subalgebras of quantum groups and of the small quantum groups, and a proof of the existence of PBW-bases that does not involve case by case considerations. The authors also include short chapter summaries at the beginning of each chapter and historical notes at the end of each chapter. The theory of Cartan graphs, Weyl groupoids, and generalized root systems appears here for the first time in a book form. Hence, the book serves as an introduction to the modern classification theory of pointed Hopf algebras for advanced graduate students and researchers working in categorial aspects and classification theory of Hopf algebras and their generalization.
Hopf Algebras and Galois Theory
Hopf Algebras and Galois 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 Hopf Algebras and Galois Theory write by Stephen U. Chase. This book was released on 2007-01-05. Hopf Algebras and Galois Theory available in PDF, EPUB and Kindle.
An Introduction to Hopf Algebras
An Introduction to 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 An Introduction to Hopf Algebras write by Robert G. Underwood. This book was released on 2011-08-30. An Introduction to Hopf Algebras available in PDF, EPUB and Kindle. Only book on Hopf algebras aimed at advanced undergraduates
