Exponential representations of matrix groups
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Exponential representations of matrix groups by Dominic G. B. Edelen

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Published by Rand Corporation in Santa Monica, Calif .
Written in English


  • Matrices.

Book details:

Edition Notes

StatementDominic G.B. Edelen.
SeriesMemorandum -- RM-5010-PR, Research memorandum (Rand Corporation) -- RM-5010-PR..
The Physical Object
Paginationv, 8 p. ;
ID Numbers
Open LibraryOL17985092M

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2. Examples of Matrix Lie Groups 10 3. Compactness 15 4. Connectedness 16 5. Simple-connectedness 18 6. Homomorphisms and Isomorphisms 19 7. Lie Groups 20 8. Exercises 22 Chapter 3. Lie Algebras and the Exponential Mapping 27 1. The Matrix Exponential 27 2. Computing the Exponential of a Matrix 29 3. The Matrix Logarithm 31 4. Further Cited by: This book focuses on matrix Lie groups and Lie algebras, and their relations and representations. This makes things a bit simpler, and not much is lost, because most of the interesting Lie groups & algebras are (isomorphic to)groups & algebras of matrices/5. In mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector example, if G is (,), the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an. Abstract. The exponential of a matrix plays a crucial role in the theory of Lie groups. The exponential enters into the definition of the Lie algebra of a matrix Lie group (Section ) and is the mechanism for passing information from the Lie algebra to the Lie by: 2.

LIE GROUPS, LIE ALGEBRAS, AND REPRESENTATIONS: AN ELEMENTARY INTRODUCTION By Brian Hall - Hardcover. $ Lie Groups Exercises 2 Lie Algebras and the Exponential Mapping The Matrix Exponential Computing the Exponential of a Matrix The Matrix Logarithm Further Properties of the Matrix Exponential The Lie Algebra of 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.   Review: Brian C. Hall’s book “Lie Groups, Lie Algebras, and Representations: An Elementary Introduction” Second Edition This book is a much revised and expanded edition of the original work. Both are great reads for a graduate student in mathematics or physics to learn Lie theory.   Preface Part I General Theory 1 Matrix Lie Groups Definition of a Matrix Lie Group Examples of Matrix Lie Groups Compactness Connectedness Simple Connectedness Homomorphisms and Isomorphisms (Optional) The Polar Decomposition for $ {SL}(n; {R})$ and $ {SL}(n; {C})$ Lie Groups Exercises 2 Lie Algebras and the Exponential Mapping The 4/5(18).

The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight. Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often. Matrix groups. Lie algebras of matrix groups; Linear algebra; Matrix groups with real entries; Representations in spacetime. It turns out that with the reversed signature we have to reverse the signs in the exponential in order to keep the angles those of the corresponding rotation and boost, so the two Weyl reps end up keeping the same.   This is an excellent presentation of Lie groups, Lie algebras and their representations for people who don't know differential geometry. To people who do know differential geometry, a Lie group is (roughly) a group that's also a smooth manifold, and a Lie algebra is a vector space with a Lie bracket. There's a Lie algebra associated with each Lie group, because there's a natural way to define.