Lectures on Lie Groups and Lie Algebras
Three of the leading figures in the field have composed this excellent introduction to the theory of Lie groups and Lie algebras. Together these lectures provide an elementary account of the theory that is unsurpassed. In the first part, Roger Carter concentrates on Lie algebras and root systems. In the second Graeme Segal discusses Lie groups. And in the final part, Ian Macdonald gives an introduction to special linear groups. Graduate students requiring an introduction to the theory of Lie groups and their applications should look no further than this book.
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Lie Groups and Lie Algebras I: Foundations of Lie Theory Lie Transformation ...
A. L. Onishchik
No preview available - 1993
abelian affine algebraic varieties algebra g automorphism basis bijective Borel subgroup Caig(G called Cartan subalgebra Chapter Chevalley closed subgroup commutative compact group conjugate connected cosets decomposition defined denote dimension dimensional representation Dynkin diagram elements example finite dimensional follows formula functions fundamental roots G acts g-module GLn(K GLnC hence homogeneous space homomorphism ideal inner product integral invariant irreducible representations isomorphic isotropy group kernel Kfin Killing form Let G Lie group linear algebraic group linear map manifold matrices matrix group maximal compact subgroup maximal tori modules morphism multiplication n x n matrices nilpotent non-empty open open sets open subset orthogonal polynomial projective variety Proof quotient representation of G representation theory root system semisimple simple groups simple Lie algebras SL2R smooth solvable subgroup of G subspace surjective symmetric tangent space theorem topological space topology torus Tx(X unipotent unique vector space weight x e G