Springer, 2019. — 312 p. — (Infosys Science Foundation Series). — ISBN: 9811332207. This book explores certain structures of fuzzy Lie algebras, fuzzy Lie superalgebras and fuzzy n-Lie algebras. In addition, it applies various concepts to Lie algebras and Lie superalgebras, including type-1 fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued...
Springer, 2019. — 312 p. — (Infosys Science Foundation Series). — ISBN: 9811332207. This book explores certain structures of fuzzy Lie algebras, fuzzy Lie superalgebras and fuzzy n-Lie algebras. In addition, it applies various concepts to Lie algebras and Lie superalgebras, including type-1 fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued...
Berlin: de Gruyter, 2021. — 542 p. This updated edition of a classic title studies identical relations in Lie algebras and also in other classes of algebras, a theory with over 40 years of development in which new methods and connections with other areas of mathematics have arisen. New topics covered include graded identities, identities of algebras The basic theory of Lie...
De Gruyter, 1992, 260p, 9783110851205. Frontmatter. Basic facts about Lie superalgebras. The structure of free Lie superalgebras. Composition techniques in the theory of Lie superalgebras. Identities in enveloping algebras. Irreducible representations of Lie superalgebras. Finiteness conditions for color Lie superalgebras with identities.
Cambridge University Press, 2005. — 652 p. — (Cambridge studies in advanced mathematics 96). — ISBN13: 9780511130830. Lie algebras have many varied applications, both in mathematics and mathematical physics. This book provides a thorough but relaxed mathematical treatment of the subject, including both the Cartan-Killing-Weyl theory of finite dimensional simple algebras and the...
Springer-Verlag London Limited 2006, 254 c Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear...
Academic Press, 2000. - 410 p. This book is a detailed reference on Lie algebras and Lie superalgebras presented in the form of a dictionary. It is intended to be useful to mathematical and theoretical physicists, from the level of the graduate student upwards. The Dictionary will serve as the reference of choice for practitioners and students alike.
Cambridge University Press, 1997,461 p. This is an introduction to Lie algebras and their applications in physics. First illustrating how Lie algebras arise naturally from symmetries of physical systems, the book then gives a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie...
Cambridge University Press, 1995. — 448 p. — (Cambridge Monographs on Mathematical Physics). — ISBN: 9780521484121. This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The...
Springer, 2019. — 563 p. — (Progress in Mathematics 330). — ISBN: 978-3-030-23530-7. This volume, a celebration of Anthony Joseph’s fundamental influence on classical and quantized representation theory, explores a wide array of current topics in Lie theory by experts in the area. The chapters are based on the 2017 sister conferences titled “Algebraic Modes of Representations,”...
Dover Publications, Inc. New York, 1979, 331 p. Chapter I Basic Concepts. Chapter II Solvable and Nilpotent Lie Algebras. Chapter III Cartan's Criterion and Its Consequences. Chapter IV Split Semi-simple Lie Algebras. Chapter V Universal Enveloping Algebras. Chapter VI The Theorem of Ado-Iwasawa. Chapter VII Classification of Irreducible Modules. Chapter VIII Characters of the...
Springer, 2012. — 244 p. — (Progress in Mathematics 295). — ISBN: 0817682732. This volume consists of expository and research articles that highlight the various Lie algebraic methods used in mathematical research today. Key topics discussed include spherical varieties, Littelmann Paths and Kac–Moody Lie algebras, modular representations, primitive ideals, representation theory...
Trollrike/Forsmobo AB Sweden, 2009. - 536 p. - ISBN: 978-969-9236-03-7, eBook, English. (Abdus Salam School of Mathematical Sciences Lahore, Pakistan). Summary. This volume contains . (1) introduction into representation theory of simple Lie superalgebras (by J. Bernstein, P. Grozman, D. Leites, and I. Shchepochkina); (2) introduction into representation theory of simple...
European Mathematical Society, 2018. — 345 p. — (EMS Textbooks in Mathematics). — ISBN: 978-3-03719-187-3. The interest for Kac–Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it also the need for an introductory textbook on the topic. The aims of this book are twofold : - to offer an accessible,...
New York: Marcel Dekker Inc, 1982. — 334 p. The nature of applications of semisimple Lie algebras and groups frequently requires the knowledge of how representations of an algebra reduce to representations of its subalgebras. The problem, although fairly standard from the point of view of mathematics, has no known easy general solution. There arises therefore a need to compile...
Montreal: Centre de Recherches Mathématiques, Université de Montréal, 1990. — 337 p. Introduction to the Series Properties of Simple Lie Algebras and their Representations Cartan matrix Determinant of the Cartan Matrix Coxeter-Dynkin Diagram Roots Fundamental Weights The Highest Weight Weight System of a Representation Weights Weyl Group Orbits Multiplicities of Weights...
Berlin: Springer-Verlag, 1979. — x+272 p. — (Lecture Notes in Mathematics, 716) The theory of Lie superalgebras (or, as they are also called, Z_2-graded Lie algebras) has undergone a remarkable evolution during the last few years. At present the most important result in the theory seems to be the classification by V.G. Kac of the finite-dimensional simple Lie superalgebras over...
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