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＜電子ブック＞
Quantum Groups and Their Primitive Ideals / by Anthony Joseph
(Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics. ISSN:21975655 ; 29)

版	1st ed. 1995.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	1995
本文言語	英語
大きさ	IX, 383 p : online resource
冊子体	Quantum groups and their primitive ideals / Anthony Joseph ; : gw,: us
著者標目	*Joseph, Anthony author SpringerLink (Online service)
件　名	LCSH:Nonassociative rings LCSH:Associative rings LCSH:Associative algebras LCSH:Topological groups LCSH:Lie groups LCSH:Algebraic geometry LCSH:Mathematical physics FREE:Non-associative Rings and Algebras FREE:Associative Rings and Algebras FREE:Topological Groups and Lie Groups FREE:Algebraic Geometry FREE:Theoretical, Mathematical and Computational Physics
一般注記	I. Hopf Algebras -- 1.1 Axioms of a Hopf Algebra -- 1.2 Group Algebras and Enveloping Algebras -- 1.3 Adjoint Action -- 1.4 The Hopf Dual -- 1.5 Comments and Complements -- 2. Excerpts from the Classical Theory -- 2.1 Lie Algebras -- 2.2 Algebraic Lie Algebras -- 2.3 Algebraic Groups -- 2.4 Lie Algebras of Algebraic Groups -- 2.5 Comments and Complements -- 3. Encoding the Cartan Matrix -- 3.1 Quantum Weyl Algebras -- 3.2 The Drinfeld Double -- 3.3 The Rosso Form and the Casimir Invariant -- 3.4 The Classical Limit and the Shapovalev Form -- 3.5 Comments and Complements -- 4. Highest Weight Modules -- 4.1 The Jantzen Filtration and Sum Formula -- 4.2 Kac-Moody Lie Algebras -- 4.3 Integrable Modules for Uq(gc) -- 4.4 Demazure Modules and Product Formulae -- 4.5 Comments and Complements -- 5. The Crystal Basis -- 5.1 Operators in the Crystal Limit -- 5.2 Crystals -- 5.3 Ad-invariant Filtrations, Twisted Actions and the Crystal Basis for Uq(n-) -- 5.4 The Grand Loop -- 5.5 Comments and Complements -- 6. The Global Bases -- 6.1 The ? Operation and the Embedding Theorem -- 6.2 Globalization -- 6.3 The Demazure Property -- 6.4 Littelmann’s Path Crystals -- 6.5 Comments and Complements -- 7. Structure Theorems for Uq(g) -- 7.1 Local Finiteness for the Adjoint Action -- 7.2 Positivity of the Rosso Form -- 7.3 The Separation Theorem -- 7.4 Noetherianity -- 7.5 Comments and Complements -- 8. The Primitive Spectrum of Uq(g) -- 8.1 The Poincaré Series of the Harmonic Space -- 8.2 Factorization of the Quantum PRV Determinants -- 8.3 Verma Module Annihilators -- 8.4 Equivalence of Categories -- 8.5 Comments and Complements -- 9. Structure Theorems for Rq[G] -- 9.1 Commutativity Relations -- 9.2 Surjectivity and Injectivity Theorems -- 9.3 The Adjoint Action -- 9.4 The R-Matrix -- 9.5 Comments and Complements -- 10. The PrimeSpectrum of Rq[G] -- 10.1 Highest Weight Modules -- 10.2 The Quantum Weyl Group -- 10.3 Prime and Primitive Ideals of Rq[G] -- 10.4 Hopf Algebra Automorphisms -- 10.5 Comments and Complements -- A.2 Excerpts from Ring Theory -- A.3 Combinatorial Identities and Dimension Theory -- A.4 Remarks on Constructions of Quantum Groups -- A.5 Comments and Complements -- Index of Notation by a more general quadratic algebra (possibly obtained by deformation) and then to derive Rq [G] by requiring it to possess the latter as a comodule. A third principle is to focus attention on the tensor structure of the cat­ egory of (!; modules. This means of course just defining an algebra structure on Rq[G]; but this is to be done in a very specific manner. Concretely the category is required to be braided and this forces (9.4.2) the existence of an "R-matrix" satisfying in particular the quantum Yang-Baxter equation and from which the algebra structure of Rq[G] can be written down (9.4.5). Finally there was a search for a perfectly self-dual model for Rq[G] which would then be isomorphic to Uq(g). Apparently this failed; but V. G. Drinfeld found that it could be essentially made to work for the "Borel part" of Uq(g) denoted U (b) and further found a general construction (the Drinfeld double) q mirroring a Lie bialgebra. This gives Uq(g) up to passage to a quotient. One of the most remarkable aspects of the above superficially different ap­ proaches is their extraordinary intercoherence. In particular they essentially all lead for G semisimple to the same and hence "canonical", objects Rq[G] and Uq(g), though this epithet may as yet be premature Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-642-78400-2

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