Primeness of Enveloping Algebras
Author: Mark Curtis Wilson
Publisher:
Published: 1995
Total Pages: 162
ISBN-13:
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Author: Mark Curtis Wilson
Publisher:
Published: 1995
Total Pages: 162
ISBN-13:
DOWNLOAD EBOOKAuthor: Jacques Dixmier
Publisher: Springer Science & Business
Published: 1996
Total Pages: 404
ISBN-13: 9780821805602
DOWNLOAD EBOOKThis is an English edition of Dixmier's book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Dixmier was awarded the Leroy P. Steele prize for expository writing in mathematics. The Committee's citation described this as one of Dixmier's "extraordinary books". Written with unique precision and elegance, the book provides the reader with insight and understanding of this very important subject. It can be an excellent textbook for a graduate course, as well as a very useful source of references in the theory of universal enveloping algebras, the area of mathematics that remains as important today as it was 20 years ago. For the 1996 edition the author updated the status of open problems and added some relevant references.
Author: William M. McGovern
Publisher: American Mathematical Soc.
Published: 1994
Total Pages: 82
ISBN-13: 0821825801
DOWNLOAD EBOOKLet [Fraktur lowercase]g be a complex simple Lie algebra of classical type, [italic capital]U([Fraktur lowercase]g) its enveloping algebra. We classify the completely prime maximal spectrum of [italic capital]U([Fraktur lowercase]g). We also construct some interesting algebra extensions of primitive quotients of [italic capital]U([Fraktur lowercase]g), and compute their Goldie ranks, lengths as bimodules, and characteristic cycles. Finally, we study the relevance of these algebras to D. Vogan's program of "quantizing" covers of nilpotent orbits [script]O in [Fraktur lowercase]g[superscript]*.
Author: Diximier
Publisher: Newnes
Published: 2009-02-10
Total Pages: 393
ISBN-13: 0444110771
DOWNLOAD EBOOKEnveloping Algebras
Author: Jacques Dixmier
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 379
ISBN-13: 0821805606
DOWNLOAD EBOOKFor the graduate student, this is a masterpiece of pedagogical writing, being succinct, wonderfully self-contained and of exceptional precision. --Mathematical Reviews This book, which is the first systematic exposition of the algebraic approach to representations of Lie groups via representations of (or modules over) the corresponding universal enveloping algebras, turned out to be so well written that even today it remains one of the main textbooks and reference books on the subject. In 1992, Jacques Dixmier was awarded the Leroy P. Steele Prize for expository writing in mathematics. The Committee's citation mentioned Enveloping Algebras as one of Dixmier's ``extraordinary books''. Written with unique precision and elegance, the book provides the reader with insight and understanding of this very important subject. For the 1996 printing, Dixmier updated the status of open problems and added some relevant references. The book is suitable as a textbook for a graduate course on enveloping algebras. It is also a valuable reference for graduate students and research mathematicians interested in Lie algebras.
Author: Mathematical Sciences Research Institute (Berkeley, Calif.).
Publisher:
Published: 1988
Total Pages: 38
ISBN-13:
DOWNLOAD EBOOKAuthor: Ian Malcolm Musson
Publisher: American Mathematical Soc.
Published: 2012-04-04
Total Pages: 512
ISBN-13: 0821868675
DOWNLOAD EBOOKLie 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 Poincare-Birkhoff-Witt 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 Harish-Chandra homomorphism, the Sapovalov determinant, supersymmetric polynomials, and Schur-Weyl 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 self-contained as possible, some background material is included on Lie theory, ring theory, Hopf algebras, and combinatorics.
Author: Stefan Catoiu
Publisher:
Published: 1997
Total Pages: 236
ISBN-13:
DOWNLOAD EBOOKAuthor: Ken Brown
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 339
ISBN-13: 303488205X
DOWNLOAD EBOOKThis book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
Author: A. Yu Pirkovskii
Publisher:
Published: 2006
Total Pages: 66
ISBN-13:
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