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140122  eng 
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a 9781461381143

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1 

a Hochschild, G. P.

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0 
0 
a Basic Theory of Algebraic Groups and Lie Algebras
h Elektronische Ressource
c by G. P. Hochschild

250 


a 1st ed. 1981

260 


a New York, NY
b Springer New York
c 1981, 1981

300 


a 267 p
b online resource

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0 

a I Representative Functions and Hopf Algebras  II Affine Algebraic Sets and Groups  III Derivations and Lie Algebras  IV Lie Algebras and Algebraic Subgroups  V Semisimplicity and Unipotency  VI Solvable Groups  VII Elementary Lie Algebra Theory  VIII Structure Theory in Characteristic 0  IX Algebraic Varieties  X Morphisms of Varieties and Dimension  XI Local Theory  XII Coset Varieties  XIII Borel Subgroups  XIV Applications of Galois Cohomology  XV Algebraic Automorphism Groups  XVI The Universal Enveloping Algebra  XVII Semisimple Lie Algebras  XVIII From Lie Algebras to Groups  References

653 


a Group Theory and Generalizations

653 


a Group theory

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a Topological Groups and Lie Groups

653 


a Lie groups

653 


a Topological groups

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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0 

a Graduate Texts in Mathematics

028 
5 
0 
a 10.1007/9781461381143

856 
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0 
u https://doi.org/10.1007/9781461381143?nosfx=y
x Verlag
3 Volltext

082 
0 

a 512.2

520 


a The theory of algebraic groups results from the interaction of various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras. It is thus an ideally suitable framework for exhibiting basic algebra in action. To do that is the principal concern of this text. Accordingly, its emphasis is on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of the simple groups and their irreducible representations. In the same spirit, this exposition has been made entirely selfcontained; no detailed knowledge beyond the usual standard material of the first one or two years of graduate study in algebra is pre supposed. The chapter headings should be sufficient indication of the content and organisation of this book. Each chapter begins with a brief announcement of its results and ends with a few notes ranging from supplementary results, amplifications of proofs, examples and counterexamples through exercises to references. The references are intended to be merely suggestions for supplementary reading or indications of original sources, especially in cases where these might not be the expected ones. Algebraic group theory has reached a state of maturity and perfection where it may no longer be necessary to reiterate an account of its genesis. Of the material to be presented here, including much of the basic support, the major portion is due to Claude Chevalley
