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The Resource Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource)
Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource)
Resource Information
The item Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a selfcontained construction of the representations of compact groups, independent of Liealgebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finitedimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: “This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.” — The Mathematical Gazette
 Language

 eng
 eng
 Edition
 Second Edition.
 Extent
 1 online resource (XIII, 449 p. 79 illus., 7 illus. in color.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 Part I: General Theory.Matrix Lie Groups
 The Matrix Exponential
 Lie Algebras
 Basic Representation Theory
 The Baker–Campbell–Hausdorff Formula and its Consequences
 Part II: Semisimple Lie Algebras
 The Representations of sl(3;C).Semisimple Lie Algebras. Root Systems
 Representations of Semisimple Lie Algebras
 Further Properties of the Representations
 Part III: Compact lie Groups
 Compact Lie Groups and Maximal Tori
 The Compact Group Approach to Representation Theory
 Fundamental Groups of Compact Lie Groups
 Appendices
 Isbn
 9783319134673
 Label
 Lie Groups, Lie Algebras, and Representations : An Elementary Introduction
 Title
 Lie Groups, Lie Algebras, and Representations
 Title remainder
 An Elementary Introduction
 Statement of responsibility
 by Brian Hall
 Language

 eng
 eng
 Summary
 This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject. In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for including: a treatment of the Baker–Campbell–Hausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebras motivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3;C) an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebras a selfcontained construction of the representations of compact groups, independent of Liealgebraic arguments The second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them: an entirely new part devoted to the structure and representation theory of compact Lie groups; a complete derivation of the main properties of root systems; the construction of finitedimensional representations of semisimple Lie algebras has been elaborated; a treatment of universal enveloping algebras, including a proof of the Poincaré–Birkhoff–Witt theorem and the existence of Verma modules; complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formula. Review of the first edition: “This is an excellent book. It deserves to, and undoubtedly will, become the standard text for early graduate courses in Lie group theory ... an important addition to the textbook literature ... it is highly recommended.” — The Mathematical Gazette
 http://library.link/vocab/creatorName
 Hall, Brian
 Dewey number

 512.55
 512.482
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 IgKj4mpeQOs
 Image bit depth
 0
 Language note
 English
 LC call number

 QA252.3
 QA387
 Literary form
 non fiction
 Series statement
 Graduate Texts in Mathematics,
 Series volume
 222
 http://library.link/vocab/subjectName

 Topological Groups
 Algebra
 Cell aggregation
 Topological Groups, Lie Groups
 Nonassociative Rings and Algebras
 Manifolds and Cell Complexes (incl. Diff.Topology)
 Label
 Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Contents
 Part I: General Theory.Matrix Lie Groups  The Matrix Exponential  Lie Algebras  Basic Representation Theory  The Baker–Campbell–Hausdorff Formula and its Consequences  Part II: Semisimple Lie Algebras  The Representations of sl(3;C).Semisimple Lie Algebras. Root Systems  Representations of Semisimple Lie Algebras  Further Properties of the Representations  Part III: Compact lie Groups  Compact Lie Groups and Maximal Tori  The Compact Group Approach to Representation Theory  Fundamental Groups of Compact Lie Groups  Appendices
 Dimensions
 unknown
 Edition
 Second Edition.
 Extent
 1 online resource (XIII, 449 p. 79 illus., 7 illus. in color.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9783319134673
 Level of compression
 uncompressed
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9783319134673
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3710000000416777
 (SSID)ssj0001501575
 (PQKBManifestationID)11921016
 (PQKBTitleCode)TC0001501575
 (PQKBWorkID)11445998
 (PQKB)11731904
 (DEHe213)9783319134673
 (EXLCZ)993710000000416777
 Label
 Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Contents
 Part I: General Theory.Matrix Lie Groups  The Matrix Exponential  Lie Algebras  Basic Representation Theory  The Baker–Campbell–Hausdorff Formula and its Consequences  Part II: Semisimple Lie Algebras  The Representations of sl(3;C).Semisimple Lie Algebras. Root Systems  Representations of Semisimple Lie Algebras  Further Properties of the Representations  Part III: Compact lie Groups  Compact Lie Groups and Maximal Tori  The Compact Group Approach to Representation Theory  Fundamental Groups of Compact Lie Groups  Appendices
 Dimensions
 unknown
 Edition
 Second Edition.
 Extent
 1 online resource (XIII, 449 p. 79 illus., 7 illus. in color.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9783319134673
 Level of compression
 uncompressed
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9783319134673
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3710000000416777
 (SSID)ssj0001501575
 (PQKBManifestationID)11921016
 (PQKBTitleCode)TC0001501575
 (PQKBWorkID)11445998
 (PQKB)11731904
 (DEHe213)9783319134673
 (EXLCZ)993710000000416777
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/LieGroupsLieAlgebrasandRepresentations/PhoGEK4huw4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/LieGroupsLieAlgebrasandRepresentations/PhoGEK4huw4/">Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>