000			02582 a2200265 4500
003			OSt
005			20241016151628.0
008			241016b |||||||| |||| 00| 0 eng d
020			_a9783319374338
040			_cIISER-BPR
041			_aENG
082			_a512.482 _bHAL _223rd
100			_aHall, Brian C. _9247
222			_aMathematics
245			_aLie groups, lie algebras, and representations : _bAn elementary introduction
250			_a2nd ed.
260			_aSwitzerland: _bSpringer International Publishing, _cc2015.
300			_axiii, 449p. : _bpbk. ; _c24cm
440			_aGraduate Texts in Mathematics _vVol. 222 _9248
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. Also includes appendices, bibliographic references and subject index.
650			_aAlgebra _9249
650			_aRings _9250
650			_aLie Algebras and Groups _9251
942			_2ddc _cBK
999			_c4193 _d4193