Let G be a connected tight single Lie-group and g be the Lie algebra of G. Let Aut(G) be the self-isomorphism group of G, Aut (g) the self-isomorphism of g, and Aut(g) the self- isomorphism group of Aut(g). All concomitant representations of the form Ad(g) (g = G) form the inner self-isomorphism group Ad(g) of g. Let (., .) be the Ad(g)-invariant positive definite inner product of Ad(g) on g, g. the invariant positive definite inner product, b the Cartan subalgebra of g, AC b the root system of (y, b), and W the Weyl group corresponding to A. Determine if the following proposition is correct, and prove your conclusion. - Aut(G) = Aut(g). Aut(g) = Ad(g). - If & € Aut(g) and (b) = b, then 6 € W.

Let G be a connected tight single Lie-group and g be the Lie algebra of G. Let Aut(G) be the self-isomorphism group of G, Aut (g) the self-isomorphism of g, and Aut(g) the self- isomorphism group of Aut(g). All concomitant representations of the form Ad(g) (g = G) form the inner self-isomorphism group Ad(g) of g. Let (., .) be the Ad(g)-invariant positive definite inner product of Ad(g) on g, g. the invariant positive definite inner product, b the Cartan subalgebra of g, AC b the root system of (y, b), and W the Weyl group corresponding to A. Determine if the following proposition is correct, and prove your conclusion. - Aut(G) = Aut(g). Aut(g) = Ad(g). - If & € Aut(g) and (b) = b, then 6 € W.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Linear algebra: please correctly and handwritten also in details
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Subject: Linear Algebra
Hello, I need help with this Linear Algebra exercise, please. Thank you!
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answer c and d
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Q1/ Using binomial formula to expand (-2+B)5.
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