Titlebook: Basic Theory of Algebraic Groups and Lie Algebras; Gerhard P. Hochschild Textbook 1981 Springer-Verlag New York Inc. 1981 Algebraische Gru

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From Lie Algebras to Groups,In this final chapter, we apply the above results on Lie algebras in order to bring the Lie theory of algebraic groups over fields of characteristic 0 to a satisfactory state of completeness.

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Representative Functions and Hopf Algebras,ed here as an abstraction from the systems of functions associated with the representations of a group by automorphisms of finite-dimensional vector spaces. This leads to an initializing discussion of our main objects of study, affine algebraic groups.

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Borel Subgroups,s. This theory is based on certain families of subgroups, such as toroids and ., i.e., irreducible maximal solvable subgroups. To some extent, the consideration of Borel subgroups reduces the structure theory to that of solvable groups.

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Algebraic Automorphism Groups, .(.) with the structure of an algebraic group in such a way that . becomes a strict .(.)-variety. The example of a toroid of dimension greater than 1 shows that this is not always possible. However, good questions remain concerning suitable subgroups of .(.) or suitably restricted groups .

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Basic Theory of Algebraic Groups and Lie Algebras978-1-4613-8114-3Series ISSN 0072-5285 Series E-ISSN 2197-5612