Lie superalgebras and enveloping algebras (Record no. 565289)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02453 a2200241 4500 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220510150246.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 220509b xxu||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9780821868676 |
| 040 ## - CATALOGING SOURCE | |
| Transcribing agency | IIT Kanpur |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 510 |
| Item number | M977l |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Musson, Ian M. |
| 245 ## - TITLE STATEMENT | |
| Title | Lie superalgebras and enveloping algebras |
| Statement of responsibility, etc | Ian M. Musson |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher | American Mathematical Society |
| Year of publication | 2012 |
| Place of publication | Providence |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xx, 488p |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE | |
| Title | Graduate Studies in Mathematics |
| 490 ## - SERIES STATEMENT | |
| Series statement | v. 131 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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 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. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Universal enveloping algebras |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Lie superalgebras |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | Books |
| Withdrawn status | Lost status | Damaged status | Not for loan | Collection code | Permanent Location | Current Location | Date acquired | Source of acquisition | Cost, normal purchase price | Full call number | Accession Number | Cost, replacement price | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| General Stacks | PK Kelkar Library, IIT Kanpur | PK Kelkar Library, IIT Kanpur | 2022-05-17 | 102 | 5365.17 | 510 M977l | A185710 | 7153.56 | Books |