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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction - Couverture rigide
Livre 144 sur 180: Graduate Texts in Mathematics
Synopsis
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 tothe textbook literature ... it is highly recommended.
-- The Mathematical Gazette
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l'auteur
Brian Hall is Professor of Mathematics at the University of Notre Dame, IN.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics, 222)
Edité par
Springer, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
Ancien ou d'occasion
Couverture rigide
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Lie Groups, Lie Algebras, and Representations : An Elementary Introduction
Edité par
Springer, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
Ancien ou d'occasion
Couverture rigide
Vendeur : GreatBookPrices, Columbia, MD, Etats-Unis
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Edité par
Springer International Publishing AG, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
Ancien ou d'occasion
Couverture rigide
Vendeur : World of Books (was SecondSale), Montgomery, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Hardback. Etat : Very Good. 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 algebrasmotivation 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 algebrasa self-contained construction of the representations of compact groups, independent of Lie-algebraic argumentsThe 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 tothe textbook literature . it is highly recommended.? The Mathematical Gazette. N° de réf. du vendeur 00105510481
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Edité par
Springer International Publishing AG, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
Ancien ou d'occasion
Couverture rigide
Vendeur : World of Books (was SecondSale), Montgomery, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Hardback. Etat : Good. 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 algebrasmotivation 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 algebrasa self-contained construction of the representations of compact groups, independent of Lie-algebraic argumentsThe 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 tothe textbook literature . it is highly recommended.? The Mathematical Gazette. N° de réf. du vendeur 00110388164
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Lie Groups, Lie Algebras, and Representations (eng)
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Edité par
Springer International Publishing AG, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
Ancien ou d'occasion
Couverture rigide
Vendeur : World of Books Inc, Montgomery, IL, Etats-Unis
Évaluation du vendeur 4 sur 5 étoiles
Hardback. Etat : Very Good. 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 algebrasmotivation 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 algebrasa self-contained construction of the representations of compact groups, independent of Lie-algebraic argumentsThe 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 tothe textbook literature . it is highly recommended.? The Mathematical Gazette. N° de réf. du vendeur CIN3319134663VG
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Edité par
Springer International Publishing AG, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
Ancien ou d'occasion
Couverture rigide
Vendeur : World of Books Inc, Montgomery, IL, Etats-Unis
Évaluation du vendeur 4 sur 5 étoiles
Hardback. Etat : Good. 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 algebrasmotivation 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 algebrasa self-contained construction of the representations of compact groups, independent of Lie-algebraic argumentsThe 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 tothe textbook literature . it is highly recommended.? The Mathematical Gazette. N° de réf. du vendeur CIN3319134663G
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Lie Groups, Lie Algebras, and Representations : An Elementary Introduction
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Lie Groups, Lie Algebras, and Representations
Edité par
Springer-Verlag GmbH, 2015
ISBN 10 : 3319134663
ISBN 13 : 9783319134666
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Lie Groups, Lie Algebras, and Representations: An Elementary Introduction: 222 (Graduate Texts in Mathematics, 222)
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