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Classification of Orbit Closures of 4-Dimensional Complex Lie Algebras

✍ Scribed by Dietrich Burde; Christine Steinhoff

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 100 KB
Volume: 214
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7714

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✦ Synopsis

Let L L ‫ރ‬ be the variety of complex n-dimensional Lie algebras. The group n Ž .

Ž . GL ‫ރ‬ acts on it via change of basis. An orbit O under this action consists of n all structures isomorphic to . The aim of this paper is to give a complete classification of orbit closures of 4-dimensional Lie algebras, i.e., determining all Ž . g O where g L L ‫ރ‬ . Starting with a classification of complex Lie algebras Ž .

4

of dimension n F 4, we study the behavior of several Lie algebra invariants under degeneration, i.e., under transition to the orbit closure. As a corollary, we will show Ž . that all degenerations in L L ‫ރ‬ can be realized via a one-parameter subgroup, but 3

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