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020 _a9783319134673
_9978-3-319-13467-3
024 7 _a10.1007/978-3-319-13467-3
_2doi
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072 7 _aMAT014000
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082 0 4 _a512.55
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082 0 4 _a512.482
_223
100 1 _aHall, Brian.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLie Groups, Lie Algebras, and Representations
_h[electronic resource] :
_bAn Elementary Introduction /
_cby Brian Hall.
250 _a2nd ed. 2015.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXIII, 449 p. 79 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v222
505 0 _aPart 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.
520 _aThis 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.
650 0 _aTopological groups.
650 0 _aLie groups.
650 0 _aNonassociative rings.
650 0 _aRings (Algebra).
650 0 _aManifolds (Mathematics).
650 0 _aComplex manifolds.
650 1 4 _aTopological Groups, Lie Groups.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11132
650 2 4 _aNon-associative Rings and Algebras.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11116
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0https://scigraph.springernature.com/ontologies/product-market-codes/M28027
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319134680
776 0 8 _iPrinted edition:
_z9783319134666
776 0 8 _iPrinted edition:
_z9783319374338
830 0 _aGraduate Texts in Mathematics,
_x0072-5285 ;
_v222
856 4 0 _uhttps://doi.org/10.1007/978-3-319-13467-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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