國立虎尾科技大學 |

Lie Groups, Lie Algebras, and Representations = An Elementary Introduction /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Lie Groups, Lie Algebras, and Representations/ by Brian Hall.
Reminder of title:	An Elementary Introduction /
Author:	Hall, Brian.
Description:	XIII, 449 p. 79 illus., 7 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Topological groups. -
Online resource:	https://doi.org/10.1007/978-3-319-13467-3
ISBN:	9783319134673

Lie Groups, Lie Algebras, and Representations = An Elementary Introduction /
Hall, Brian.

Lie Groups, Lie Algebras, and RepresentationsAn Elementary Introduction /[electronic resource] :by Brian Hall. - 2nd ed. 2015. - XIII, 449 p. 79 illus., 7 illus. in color.online resource. - Graduate Texts in Mathematics,2220072-5285 ;. - Graduate Texts in Mathematics,222.

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.

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.

ISBN: 9783319134673

Standard No.: 10.1007/978-3-319-13467-3doiSubjects--Topical Terms:

885827
Topological groups.

LC Class. No.: QA252.3

Dewey Class. No.: 512.55

Lie Groups, Lie Algebras, and Representations = An Elementary Introduction /
LDR:04065nam a22004335i 4500 001 960821
003 DE-He213
005 20200703140212.0
007 cr nn 008mamaa
008 201211s2015 gw | s |||| 0|eng d
020 $a 9783319134673 $9 978-3-319-13467-3
024 7 $a 10.1007/978-3-319-13467-3 $2 doi
035 $a 978-3-319-13467-3
050 4 $a QA252.3
050 4 $a QA387
072 7 $a PBG $2 bicssc
072 7 $a MAT014000 $2 bisacsh
072 7 $a PBG $2 thema
082 0 4 $a 512.55 $2 23
082 0 4 $a 512.482 $2 23
100 1 $a Hall, Brian. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1254914
245 1 0 $a Lie Groups, Lie Algebras, and Representations $h [electronic resource] : $b An Elementary Introduction / $c by Brian Hall.
250 $a 2nd ed. 2015.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a XIII, 449 p. 79 illus., 7 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 222
505 0 $a 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.
520 $a 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.
650 0 $a Topological groups. $3 885827
650 0 $a Lie groups. $3 527929
650 0 $a Nonassociative rings. $3 1254916
650 0 $a Rings (Algebra). $3 685051
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Complex manifolds. $3 676705
650 1 4 $a Topological Groups, Lie Groups. $3 672074
650 2 4 $a Non-associative Rings and Algebras. $3 672285
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology). $3 668590
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319134680
776 0 8 $i Printed edition: $z 9783319134666
776 0 8 $i Printed edition: $z 9783319374338
830 0 $a Graduate Texts in Mathematics, $x 0072-5285 ; $v 222 $3 1254915
856 4 0 $u https://doi.org/10.1007/978-3-319-13467-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)