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On completeness of holomorphic principal bundles

Published online by Cambridge University Press:  22 January 2016

Shigeru Takeuchi
Shigeru Takeuchi*
Affiliation:
Gifu University
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In this paper we shall investigate the structure of complex Lie groups from function theoretical points of view. A. Morimoto proved in [10] that every connected complex Lie group G has the smallest closed normal connected complex Lie subgroup Ge, such that the factor group G/Ge is Stein. On the other hand there hold the following two basic structure theorems (A1) and (A2) for a connected algebraic group G (cf. [12]). (A1): G has the smallest normal algebraic subgroup N such that the factor group G/N is an affine algebraic group. Moreover N is a connected central subgroup. (A2): G has the unique maximal connected affine algebraic subgroup L, where L is normal and the factor group G/L is an abelian variety.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 121 - 138
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

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