Root Systems of Levi Type for Lie Algebras of Affine Type
Author: Zahra Behrang
Publisher:
Published: 2014
Total Pages: 0
ISBN-13:
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Classification and Structure Theory of Lie Algebras of Smooth Sections
Author: Hasan Gündoğan
Publisher: Logos Verlag Berlin GmbH
Published: 2011
Total Pages: 172
ISBN-13: 383253024X
DOWNLOAD EBOOKLie groups and their "derived objects", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on the structure of finite-dimensional Lie algebras, the classification and structure theory of infinite-dimensional Lie algebras has become an interesting and fairly vast field of interest. This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.
Lie Algebras of Finite and Affine Type
Author: Roger William Carter
Publisher: Cambridge University Press
Published: 2005-10-27
Total Pages: 662
ISBN-13: 9780521851381
DOWNLOAD EBOOKThis book provides a thorough but relaxed mathematical treatment of Lie algebras.
Integral Bases for Affine Lie Algebras and Their Universal Enveloping Algebras
Author: David Mitzman
Publisher: American Mathematical Soc.
Published: 1985
Total Pages: 170
ISBN-13: 0821850431
DOWNLOAD EBOOKA revised version of the author's PhD thesis written under the supervision of J Lepowsky at Rutgers University in 1983.
Lie Algebras, Geometry, and Toda-Type Systems
Author: Alexander Vitalievich Razumov
Publisher: Cambridge University Press
Published: 1997-05-15
Total Pages: 271
ISBN-13: 0521479231
DOWNLOAD EBOOKThe book describes integrable Toda type systems and their Lie algebra and differential geometry background.
Representations of Finite Groups of Lie Type
Author: François Digne
Publisher: Cambridge University Press
Published: 2020-03-05
Total Pages: 267
ISBN-13: 1108481485
DOWNLOAD EBOOKAn up-to-date and self-contained introduction based on a graduate course taught at the University of Paris.
Linear Algebraic Groups and Finite Groups of Lie Type
Author: Gunter Malle
Publisher: Cambridge University Press
Published: 2011-09-08
Total Pages: 324
ISBN-13: 113949953X
DOWNLOAD EBOOKOriginating from a summer school taught by the authors, this concise treatment includes many of the main results in the area. An introductory chapter describes the fundamental results on linear algebraic groups, culminating in the classification of semisimple groups. The second chapter introduces more specialized topics in the subgroup structure of semisimple groups and describes the classification of the maximal subgroups of the simple algebraic groups. The authors then systematically develop the subgroup structure of finite groups of Lie type as a consequence of the structural results on algebraic groups. This approach will help students to understand the relationship between these two classes of groups. The book covers many topics that are central to the subject, but missing from existing textbooks. The authors provide numerous instructive exercises and examples for those who are learning the subject as well as more advanced topics for research students working in related areas.
Representations of Affine Lie Algebras
Author: V. Futorny
Publisher: Queens University, Institute of Intergovernmental Relations
Published: 1997
Total Pages: 108
ISBN-13:
DOWNLOAD EBOOKApplying the Classification of Finite Simple Groups
Author: Stephen D. Smith
Publisher: American Mathematical Soc.
Published: 2018-04-30
Total Pages: 248
ISBN-13: 1470442914
DOWNLOAD EBOOKClassification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications
Author: Yun Gao
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 314
ISBN-13: 0821845071
DOWNLOAD EBOOKThis volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.
