ORPP logo

Quantum Linear Groups. (Record no. 69490)

MARC details
000 -LEADER
fixed length control field 05810nam a22004933i 4500
001 - CONTROL NUMBER
control field EBC3113959
003 - CONTROL NUMBER IDENTIFIER
control field MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20240729124555.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m o d |
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cnu||||||||
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 240724s1991 xx o ||||0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781470408626
Qualifying information (electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9780821825013
035 ## - SYSTEM CONTROL NUMBER
System control number (MiAaPQ)EBC3113959
035 ## - SYSTEM CONTROL NUMBER
System control number (Au-PeEL)EBL3113959
035 ## - SYSTEM CONTROL NUMBER
System control number (CaPaEBR)ebr10918912
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)922981643
040 ## - CATALOGING SOURCE
Original cataloging agency MiAaPQ
Language of cataloging eng
Description conventions rda
-- pn
Transcribing agency MiAaPQ
Modifying agency MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA171 -- .P377 1991eb
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512/.2
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Wang, J.
245 10 - TITLE STATEMENT
Title Quantum Linear Groups.
250 ## - EDITION STATEMENT
Edition statement 1st ed.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Providence :
Name of producer, publisher, distributor, manufacturer American Mathematical Society,
Date of production, publication, distribution, manufacture, or copyright notice 1991.
264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Date of production, publication, distribution, manufacture, or copyright notice ©1991.
300 ## - PHYSICAL DESCRIPTION
Extent 1 online resource (168 pages)
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Memoirs of the American Mathematical Society ;
Volume/sequential designation v.89
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Intro -- Contents -- Introduction -- 1. Quantum Groups -- 1.1. Quantum affine spaces -- 1.2. Quantum groups -- 1.3. Direct products -- 1.4. Closed subgroups -- 1.5. Normal closed subgroups -- 1.6. Kernels and exact sequences -- 1.7. Cartesian squares -- 1.8. Coverings -- 2. Representation Theory of Quantum Groups -- 2.1. Rational representations -- 2.2. Functorial description -- 2.3. Defining matrices -- 2.4. Contragradient modules and tensor products -- 2.5. Characters and character groups -- 2.6. Fixed points -- 2.7. Induction -- 2.8. Injective objects -- 2.9. Exact subgroups of quantum groups -- 2.10. A theorem on central faithfully flat morphisms -- 2.11. The Hochschild-Serre spectral sequence -- 3. Quantum Matrix Spaces -- 3.1. Quadratic algebras -- 3.2. Quasi-Yang-Baxter algebras -- 3.3. Basis theorem for quasi-Yang-Baxter algebras -- 3.4. The quadratic algebras K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)]] -- 3.5. The quantum matrix space M[sub(q)](n) -- 3.6. The bialgebra structure on K[M[sub(q)](n)] -- 3.7. Some automorphisms and anti-automorphisms -- 3.8. K[A[sup(n‌0)][sub(q)]] and K[A[sup(n‌0)][sub(q)] as K[M[sub(q)](n)]-comodules -- 4. Quantum Determinants -- 4.1. Quantum determinant -- 4.2. First properties of the determinant -- 4.3. Subdeterminants -- 4.4. Laplace expansions -- 4.5. Some commutators, I -- 4.6. The centrality of the determinant -- 5. The Antipode and Quantum Linear Groups -- 5.1. Some commutators, II -- 5.2. Some commutators, III -- 5.3. Quantum general and special linear groups -- 5.4. A property of the antipode -- 6. Some Closed Subgroups -- 6.1. Parabolic and Levi subgroups -- 6.2. Some properties of the parabolic and Levi subgroups -- 6.3. Some remarks -- 6.4. Coadjoint action of the maximal torus and the root system -- 6.5. Character groups of T[sub(q)] and B[sub(q)] -- 7. Frobenius Morphisms and Kernels.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 7.1. Gaussian polynomials -- 7.2. Frobenius morphisms -- 7.3. Infinitesimal subgroups -- 7.4. Some homological properties of GL[sub(q)](n) -- 7.5. Some exact subgroups of GL[sub(q)](n) -- 8. Global Representation Theory -- 8.1. Density of the "big cell -- 8.2. Highest weight modules -- 8.3. Some properties of induced G[sub(q)]-modules -- 8.4. Induction to parabolic subgroups -- 8.5. The semisimple rank 1 case, I -- 8.6. The semisimple rank 1 case, II -- 8.7. The one-to-one correspondence between irreducible modules and dominant weights -- 8.8. Formal characters and their invariance under the Weyl group -- 8.9. Injective modules for Borel subgroups -- 8.10. A finiteness theorem -- Weyl modules -- 9. Infinitesimal Representation Theory -- 9.1. An infinitesimal version of the "density theorem -- 9.2. Highest weight and irreducible representations for (G[sub(q)])[sub(1)]-T and (G[sub(q)])[sub(1)]-B -- 9.3. Irreducible representations of (G[sub(q)])[sub(1)] -- 9.4. The tensor product theorem -- 9.5. Induction to "infinitesimal Borel subgroups -- 9.6. Induction from "infinitesimal Borel subgroups", I -- 9.7. Induction from "infinitesimal Borel subgroups", II -- 9.8. Highest weight categories -- 9.9. Injective modules for (G[sub(q)])[sub(1)] -- 9.10. The Steinberg module -- 10. The Generalization of Certain Important Theorems on the Cohomology of Vector Bundles on the Flag Manifold -- 10.1. An isomorphism theorem and its consequences -- 10.2. Borel-Weil-Bott theorem for small dominant weights -- 10.3. Serre duality and strong linkage principle -- 10.4. Kempf vanishing theorem, good filtrations and Weyl character formula -- 10.5. A coalgebra isomorphism between K[GL[sub(q)](n)] and K[GL-[sub(q)](n)] -- 11. g-Schur Algebras -- 11.1. Polynomial representations of G[sub(q)] -- 11.2. The g-Schur algebra S[sub(q)](n,r).
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note 11.3. S[sub(q)](n,r) as an endomorphism algebra -- 11.4. On the complete reducibility of G[sub(q)]-modules -- 11.5. S[sub(q)](n,r) as a quasi-hereditary algebra -- 11.6. The generalization of a theorem of J. A. Green -- 11.7. Tensor product theorem for q-Schur algebras -- References.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Linear algebraic groups.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Representations of groups.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Group schemes (Mathematics).
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
Main entry heading Wang, J.
Title Quantum Linear Groups
Place, publisher, and date of publication Providence : American Mathematical Society,c1991
International Standard Book Number 9780821825013
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element ProQuest (Firm)
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Memoirs of the American Mathematical Society
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113959">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3113959</a>
Public note Click to View

No items available.

© 2024 Resource Centre. All rights reserved.