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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Graduate Texts in Mathematicshttp://image.papertrans.cn/b/image/181178.jpg

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J. A. Denev,J. Fr?hlich,H. BockhornHere, we introduce some concepts and techniques that could be described as the differential calculus of algebra and group theory. As in analysis, this is a tool for linearizing problems.

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R. Leitsmann,F. Bechstedt,F. OrtmannSection 1 is devoted to the generalities concerning simple and semisimple modules over a ring, and to the theory of a single linear endomorphism. The main result from this second area is the multiplicative . of a linear automorphism, which plays an important role in the structure theory of algebraic groups.

AFFIX

https://doi.org/10.1007/978-3-540-88303-6This chapter establishes fundamental results concerning Lie algebras over fields of characteristic 0. The principal notions involved are semisimplicity, solvability and nilpotency.

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Ping Wang,Jochen Fr?hlich,Ulrich MaasThe theme of this chapter is the use of Galois theory for extending the structure theory of algebraic groups. The applicability of Galois theory stems from the fact that solvable algebraic groups are made up from the additive and multiplicative groups of the base field, and Section 1 provides the technical preparations for exploiting this.

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Derivations and Lie Algebras,Here, we introduce some concepts and techniques that could be described as the differential calculus of algebra and group theory. As in analysis, this is a tool for linearizing problems.

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Elementary Lie Algebra Theory,This chapter establishes fundamental results concerning Lie algebras over fields of characteristic 0. The principal notions involved are semisimplicity, solvability and nilpotency.