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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Affine Algebraic Sets and Groups, in an algebraic group. The main result of Section 2 is the fact that algebraic subgroups are determined by their semi-invariants in the algebra of polynomial functions of the containing group. Section 3 contains the fundamental results on homomorphisms from commutative algebras to the base field, c

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Aspiration

Solvable Groups,ically closed and that the group is irreducible. In the presence of these assumptions, the solvable groups are characterized by the property that their simple polynomial modules are 1-dimensional. This is the Lie-Kolehin Theorem, given here as Theorem 1.1.

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報復(fù)

Annotate

Morphisms of Varieties and Dimension,algebra than has been used up to now. Thus, Section 1 establishes Noether’s Normalization Theorem, which is used for reducing some of the required ideal theoretical considerations to the situation of an ordinary polynomial algebra. The remaining results of Section 1 concern the connections between t

impale

Coset Varieties,ver an algebraically closed field ., and . is an algebraic subgroup of .. The main task for this chapter is the construction of an appropriate variety structure on ./.. In Section 1, it appears that [.(.)]. is a suitable candidate for the field .(./.) of rational functions. Starting with this field,

SCORE

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.

CYT