Kategoria BISAC: Mathematics >> Group Theory

This is an introduction to the mathematics behind the phrase "quantum Lie algebra." The numerous attempts over the last 15-20 years to define a quantum Lie algebra as an elegant algebraic object with a binary "quantum" Lie bracket have not been widely accepted. In this book, an alternative approach is developed that includes multivariable operations. Among the problems discussed are the following: a PBW-type theorem; quantum deformations of Kac--Moody algebras; generic and symmetric quantum Lie operations; the Nichols algebras; the Gurevich--Manin Lie algebras; and Shestakov--Umirbaev...

Ce livre des Elements de mathematique est consacre a la Topologie algebrique. Les quatre premiers chapitres presentent la theorie des revetements d'un espace topologique et du groupe de Poincare. On construit le revetement universel d'un espace connexe pointe delacable et on etablit l'equivalence de categories entre revetements de cet espace et actions du groupe de Poincare.

On demontre une version generale du theoreme de van Kampen exprimant le groupoide de Poincare d'un espace topologique comme un coegalisateur de diagrammes de groupoides. Dans de nombreuses situations...

This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.

Topics presented include:

structure and representation theory of reductive algebraic monoids

monoid schemes and applications of monoids

monoids related to Lie theory

equivariant embeddings of algebraic groups

constructions and properties of monoids from algebraic combinatorics

endomorphism monoids induced from vector bundles

Hodge-Newton decompositions of reductive...

Based on presentations given at the NordForsk Network Closing Conference "Operator Algebra and Dynamics," held in Gjaargarour, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science.

It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite...

Filling a gap in the literature, this book takes the reader to the frontiers of equivariant topology, the study of objects with specified symmetries. The discussion is motivated by reference to a list of instructive "toy" examples and calculations in what is a relatively unexplored field. The authors also provide a reading path for the first-time reader less interested in working through sophisticated machinery but still desiring a rigorous understanding of the main concepts. The subject's classical counterparts, ordinary homology and cohomology, dating back to the work of Henri Poincare...

Auf der Basis von Symmetrie-Uberlegungen bietet dieses Buch eine einzigartige Herleitung der fundamentalen Theorien der Physik. Dafur werden zunachst alle mathematische Werkzeuge eingefuhrt, die der Leser benotigt, um mit Symmetrien in der Physik zu arbeiten. Hierbei wird jedoch nur gewohnliche Schulmathematik vorausgesetzt. Anschliessend werden diese Werkzeuge benutzt, um durch Symmetrie-Uberlegungen die fundamentalen Gleichungen der Quantenmechanik, Quantenfeldtheorie, Elektrodynamik und Klassischen Mechanik herzuleiten. So ist der Leser in der Lage, die Basis-Annahmen hinter und die...

In this book, the theory of operational symmetries is developed from the numbers, from Plato's and Kepler's symmetries over the simple Lie groups to their applications...