Lie Groups, Lie Algebras, and Their Representation

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Weisstein, Eric W.


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Representation theory of Lie groups and Lie algebras - Lec 17 - Frederic Schuller

Hints help you try the next step on your own. Unlimited random practice problems and answers with built-in Step-by-step solutions. Lie groups, Lie algebras.

Fundamental examples, Heisenberg algebras. Semi-simple Lie algebras.

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Categories of representations, irreducible representations. Complete reducibility.

Structure of semi-simple Lie algebras. Root systems, Weyl group.

Lie Groups, Lie Algebras, and Representations

Representations of finite-dimensional Lie algebras. Highest weight modules, Verma modules, category O. Parametrization of simple modules. Jordan-Holder series, multiplicities.

Lie Groups, Lie Algebras, and Their Representations

Finite-dimensional representations. To present a circle of ideas around Lie groups, Lie algebras and their representations, it is necessary to make a few principal choices. The first question is how to describe a relation between Lie groups and Lie algebras. To make the book accessible to a broader audience, the author does not suppose knowledge of theory of manifolds.

Lie Groups, Lie Algebras, and Their Representation (Graduate Texts in Mathematics, Vol. 102)

He restricts the attention to matrix groups. Lie algebra of G is then defined using simple properties of the exponential map. As for the correspondence between Lie group homomorphisms and Lie algebra homomorphisms, the author is using the Baker-Campbell-Hausdorff theorem for its description.