
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Graduate Studies in Mathematics 2012; 488 pp; hardcover Volume: 131 ISBN10: 0821868675 ISBN13: 9780821868676 List Price: US$87 Member Price: US$69.60 Order Code: GSM/131 See also: Five Lectures on Supersymmetry  Daniel S Freed Enveloping Algebras  Jacques Dixmier Finite Dimensional Algebras and Quantum Groups  Bangming Deng, Jie Du, Brian Parshall and Jianpan Wang  Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. This book develops the theory of Lie superalgebras, their enveloping algebras, and their representations. The book begins with five chapters on the basic properties of Lie superalgebras, including explicit constructions for all the classical simple Lie superalgebras. Borel subalgebras, which are more subtle in this setting, are studied and described. Contragredient Lie superalgebras are introduced, allowing a unified approach to several results, in particular to the existence of an invariant bilinear form on \(\mathfrak{g}\). The enveloping algebra of a finite dimensional Lie superalgebra is studied as an extension of the enveloping algebra of the even part of the superalgebra. By developing general methods for studying such extensions, important information on the algebraic structure is obtained, particularly with regard to primitive ideals. Fundamental results, such as the PoincaréBirkhoffWitt Theorem, are established. Representations of Lie superalgebras provide valuable tools for understanding the algebras themselves, as well as being of primary interest in applications to other fields. Two important classes of representations are the Verma modules and the finite dimensional representations. The fundamental results here include the Jantzen filtration, the HarishChandra homomorphism, the Šapovalov determinant, supersymmetric polynomials, and SchurWeyl duality. Using these tools, the center can be explicitly described in the general linear and orthosymplectic cases. In an effort to make the presentation as selfcontained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics. Request an examination or desk copy. Readership Graduate students interested in Lie algebras, Lie superalgebras, quantum groups, string theory, and mathematical physics. 


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