Titlebook: Lie Groups, Lie Algebras, and Representations; An Elementary Introd Brian C. Hall Textbook 2015Latest edition Springer International Publis

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The Baker–Campbell–Hausdorff Formula and Its Consequencessociated Lie algebra notion. In this chapter, we attempt to go in the “hard” direction, from the Lie algebra to the Lie group. We will investigate three questions relating to the preceding three theorems.

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Semisimple Lie Algebrasally, in Chapter?10, we consider several additional properties of the representations constructed in Chapter?9. Meanwhile, in Chapters?11 and?12, we consider representation theory from the closely related viewpoint of compact Lie groups.

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The Representations of result of this chapter is Theorem?., which states that an irreducible finite-dimensional representation of . can be classified in terms of its “highest weight.” This result is analogous to the results of Sect.?., in which we classify the irreducible representations by the largest eigenvalue of .(.), namely the non-negative integer?..

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978-3-319-37433-8Springer International Publishing Switzerland 2015

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