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Lobachevskii Journal of Mathematics, 1999, том 3, страницы 5–17
(Mi ljm158)
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On the variety of 3-dimensional Lie algebras
Y. Agaoka Hiroshima University
Аннотация:
It is known that a 3-dimensional Lie algebra is unimodular or solvable as a result of the classification. We give a simple proof of this fact, based on a fundamental identity for 3-dimensiona Lie algebras, which was first appeared in [21]. We also give a representation
theoretic meaning of the invariant of 3-dimensional Lie algebras introduced in [15], [22], by calculating the $GL(V)$-irreducible decomposition of polynomials on the space $\wedge^2V^*\otimes V$ up to degree 3. Typical four covariants naturally appear in this decomposition, and we show that the isomorphism classes of 3-dimensional Lie algebras are completely determined by the $GL(V)$-invariant concepts in $\wedge^2V^*\otimes V$ defined by these four covariants. We also exhibit an explicit algorithm to distinguish them.
Образец цитирования:
Y. Agaoka, “On the variety of 3-dimensional Lie algebras”, Lobachevskii J. Math., 3 (1999), 5–17
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/ljm158 https://www.mathnet.ru/rus/ljm/v3/p5
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Страница аннотации: | 276 | PDF полного текста: | 152 |
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