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Algèbres de Lie kählériennes et double extension

✍ Scribed by Jean-Michel Dardié; Alberto Médina

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
250 KB
Volume
185
Category
Article
ISSN
0021-8693

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✦ Synopsis

A Kahler Lie algebra is a real Lie algebra carrying a symplectic 2-cocycle and ¨Ž Ž .. an integrable complex structure j such that x, j y is a scalar product. We give a process, called Kahler double extension, which realizes a Kahler Lie algebra as ¨ẗhe Kahler reduction of another one. We show that every Kahler algebra is ¨Ä 4 obtained by a sequence of such a process from 0 or a flat Kahler algebra; it is Ä 4 obtained from 0 iff it contained a lagrangian sub-algebra. These methods allow us to prove that any completely solvable and unimodular Kahler algebra is commuta -ẗive.

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