Lie groups: an introduction through linear groups

By:

Rossmann, Wulf

Series: Oxford Graduate Texts in Mathematics ; 5Publication details: Oxford: Oxford University Press, 2011.Description: x, 265p.: pbk.: 21cmISBN:

9780199202515

Subject(s):

DDC classification:

512.55 ROS

Summary: Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups. https://global.oup.com/academic/product/lie-groups-9780199202515?cc=in&lang=en&#

List(s) this item appears in: Oxford Graduate Texts

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	IIT Gandhinagar	General	512.55 ROS (Browse shelf(Opens below))	1	Available	035728

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Previous	512.55 PAU Completely bounded maps and operator algebras	512.55 PED C* algebras and their automorphism groups	512.55 RAG Lie groups and lie algebras	512.55 ROS Lie groups: an introduction through linear groups	512.55 SAK Operator algebras in dynamical systems, Vol. 41	512.55 SUN Invitation to von Neumann algebras	512.55 VAR Lie groups, Lie algebras, and their representations	Next

Includes References and Index

Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

https://global.oup.com/academic/product/lie-groups-9780199202515?cc=in&lang=en&#

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