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Sugawara Operators for Classical Lie Algebras

Von:

Molev, Alexander, 1961- [aut]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Mathematical Surveys and Monographs ; v. 229Verlag: Providence : American Mathematical Society, 2018Beschreibung: 1 Online-Ressource (321 pages)Schlagwörter:

Andere physische Formen: 9781470436599 | 1470443910. | 9781470443917. | Erscheint auch als: Sugawara operators for classical Lie algebras. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2018. xiv, 304 Seiten | Print version: Sugawara Operators for Classical Lie Algebras. Providence : American Mathematical Society, ©2018DDC-Klassifikation:

512/.482

MSC: MSC: *17-02 | 17B35 | 16S30 | 17B63 | 17B67 | 17B69LOC-Klassifikation:

QA252.3

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Zusammenfassung: 5.4. Symmetrizer and anti-symmetrizer for _{ }5.5. Symmetrizer and anti-symmetrizer for _{ }; 5.6. Manin matrices in types, and; 5.7. Bibliographical notes; Chapter 6. Feigin-Frenkel center; 6.1. Center of a vertex algebra; 6.2. Affine vertex algebras; 6.3. Feigin-Frenkel theorem; 6.4. Affine symmetric functions; 6.5. From Segal-Sugawara vectors to Casimir elements; 6.6. Center of the completed universal enveloping algebra; 6.7. Bibliographical notes; Chapter 7. Generators in type; 7.1. Segal-Sugawara vectors; 7.2. Sugawara operators in type; 7.3. Bibliographical notesZusammenfassung: Cover; Title page; Contents; Preface; Chapter 1. Idempotents and traces; 1.1. Primitive idempotents for the symmetric group; 1.2. Primitive idempotents for the Brauer algebra; 1.3. Traces on the Brauer algebra; 1.4. Tensor notation; 1.5. Action of the symmetric group and the Brauer algebra; 1.6. Bibliographical notes; Chapter 2. Invariants of symmetric algebras; 2.1. Invariants in type; 2.2. Invariants in types, and; 2.3. Symmetrizer and extremal projector; 2.4. Bibliographical notes; Chapter 3. Manin matrices; 3.1. Definition and basic properties; 3.2. Identities and invertibilityZusammenfassung: Chapter 10. Yangian characters in type10.1. Yangian for _{ }; 10.2. Dual Yangian for _{ }; 10.3. Double Yangian for _{ }; 10.4. Invariants of the vacuum module over the double Yangian; 10.5. From Yangian invariants to Segal-Sugawara vectors; 10.6. Screening operators; 10.7. Bibliographical notes; Chapter 11. Yangian characters in types, and; 11.1. Yangian for _{ }; 11.2. Dual Yangian for _{ }; 11.3. Screening operators; 11.4. Bibliographical notes; Chapter 12. Classical -algebras; 12.1. Poisson vertex algebras; 12.2. Generators of ()Zusammenfassung: The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algePPN: PPN: 1032016906Package identifier: Produktsigel: ZDB-4-NLEBK

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