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)

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
Creator
Author
Author
Subject
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 self-contained construction of the representations of compact groups, independent of Lie-algebraic 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 finite-dimensional 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
Member of
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
  • Non-associative 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)
Instantiates
Publication
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
10.1007/978-3-319-13467-3
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
  • (DE-He213)978-3-319-13467-3
  • (EXLCZ)993710000000416777
Label
Lie Groups, Lie Algebras, and Representations : An Elementary Introduction, by Brian Hall, (electronic resource)
Publication
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
10.1007/978-3-319-13467-3
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
  • (DE-He213)978-3-319-13467-3
  • (EXLCZ)993710000000416777

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