04639nam a22005295i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153050001000165072001600175072002300191072001500214082001500229082001600244100007400260245012100334250001800455264007500473300006500548336002600613337002600639338003600665347002400701490005300725505056700778520199801345650002403343650001603367650002603383650002103409650002903430650002303459650011203482650011603594650013203710710003403842773002603876776003603902776003603938776003603974830005304010856004604063978-3-319-13467-3DE-He21320210602114659.0cr nn 008mamaa150511s2015 gw | s |||| 0|eng d a97833191346737 a10.1007/978-3-319-13467-32doi 4aQA252.3 4aQA387 7aPBG2bicssc 7aMAT0140002bisacsh 7aPBG2thema04a512.5522304a512.4822231 aHall, Brian.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aLie Groups, Lie Algebras, and Representationsh[electronic resource] :bAn Elementary Introduction /cby Brian Hall. a2nd ed. 2015. 1aCham :bSpringer International Publishing :bImprint: Springer,c2015. aXIII, 449 p. 79 illus., 7 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aGraduate Texts in Mathematics,x0072-5285 ;v2220 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. 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. 0aTopological groups. 0aLie groups. 0aNonassociative rings. 0aRings (Algebra). 0aManifolds (Mathematics). 0aComplex manifolds.14aTopological Groups, Lie Groups.0https://scigraph.springernature.com/ontologies/product-market-codes/M1113224aNon-associative Rings and Algebras.0https://scigraph.springernature.com/ontologies/product-market-codes/M1111624aManifolds and Cell Complexes (incl. Diff.Topology).0https://scigraph.springernature.com/ontologies/product-market-codes/M280272 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978331913468008iPrinted edition:z978331913466608iPrinted edition:z9783319374338 0aGraduate Texts in Mathematics,x0072-5285 ;v22240uhttps://doi.org/10.1007/978-3-319-13467-3