On the intersection of irreducible components of the space of finite-dimensional Lie algebras

Journal Article · Tue Jul 31 00:00:00 EDT 2012 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2012V203N07ABEH004250· OSTI ID:22094072

Gorbatsevich, Vladimir V ^[1]

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1. Moscow State Aviation Technological University, Moscow (Russian Federation)

The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.

• OSTI ID: 22094072
• Journal Information: Sbornik. Mathematics, Vol. 203, Issue 7; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
LIE GROUPS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL SPACE
SPECTRA