Lie superalgebras and enveloping algebras
 Author/Creator
 Musson, Ian M. (Ian Malcolm), 1953
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xx, 488 p. : ill ; 27 cm.
 Series
 Graduate studies in mathematics ; v. 131.
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Available online

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QA252.3 .M87 2012

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QA252.3 .M87 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 471484) and index.
 Publisher's Summary
 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 PoincareBirkhoffWitt 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 Sapovalov 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Ian M. Musson.
 Series
 Graduate studies in mathematics ; v. 131
 ISBN
 9780821868676
 0821868675