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Toroidal Groups - Line Bundles, Cohomology and Quasi-Abelian Varieties (Paperback, 2001 ed.)
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Toroidal Groups - Line Bundles, Cohomology and Quasi-Abelian Varieties (Paperback, 2001 ed.)
Series: Lecture Notes in Mathematics, 1759
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Lie linksbetweentorus and Toroidal arethe complex missing groups
any groups such and of Lie as complex pseudoconvexity groups.
Manyphenomena groups the of beunderstood thestructure can
onlythrough concept cohomologygroups of different behavior ofthe
oftoroidal The cohomology complex groups groups. the of their
toroidal Lie be characterized can by properties groups - groups in
their centers. pearing book. So the oldest have not been treated in
a Toroidal systematically groups in it who worked in this field and
the mathematician youngest working living aboutthemain results
these decidedto a concerning comprehensivesurvey give and to
discuss problems. open groups of the torus As the Toroidal are
generalization groups. groups non-compact and Grauert. As in the
sense ofAndreotti manifolds are convex complex they others have
similarbehaviorto Lie someofthem a complextori, complex groups
whencec- different with for non-Hausdorff are example cohomology
groups, mustbe used. newmethods pletely of is to describe the
fundamental The aim of these lecture notes properties the
reductiontheorem toroidal As a result ofthe qua- meromorphic
groups. basic ends inthethird varieties of interest.Their Abelian
are special description MainTheorem. withthe chapter wide atthe -
ofSOPHus LIE -wasintroducedtoa This inhonour public theory " 1999.
after Lie" in on Conference 100Years Leipzig, July 8-9, Sophus
HUMBOLDT wishes to thank the ALEXANDER VON The first-named author
FOUNDATION for partial support. December 1998 Hannoverand Toyama,
YukitakaAbeandKlaus Kopfermann Contents 1 Introduction
..................................................... of Toroidal 3
1. The Concept Groups ............................. 1.1 and
toroidal coordinates 3 Irrationality ........................
Toroidal 3 ........................................... groups 7
Complex homomorphisms .................................. Toroidal
coordinates and C*n-q -fibre bundles 9 .................
General
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