Completable filiform Lie algebras
نویسندگان
چکیده
منابع مشابه
Simple completable contractions of nilpotent Lie algebras
We study a certain class of non-maximal rank contractions of the nilpotent Lie algebra gm and show that these contractions are completable Lie algebras. As a consequence a family of solvable complete Lie algebras of non-maximal rank is given in arbitrary dimension. . AMS Math. Subj. Class. 17B10, 17B30.
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We classify the cohomology spaces H(g,K) for all filiform nilpotent Lie algebras of dimension n ≤ 11 over K and for certain classes of algebras of dimension n ≥ 12. The result is applied to the determination of affine cohomology classes [ω] ∈ H(g,K). We prove the general result that the existence of an affine cohomology class implies an affine structure of canonical type on g, hence a canonical...
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The aim of this note is to prove that every non characteristically nilpotent filiform algebra is provided with an affine structure. We generalize this result to the class of nilptent algebras whose derived algebra admits non singular derivation.
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The present paper offers the classification of naturally graded p filiform Lie algebras in arbitrary finite dimension n . For sufficiently high n , (n ≥ max{3p − 1, p + 8}), and for all admissible value of p the results are a generalization of Vergne’s in case of filiform Lie algebras [11]. Mathematics subject classification 2000: 22E60, 17B30, 17B70
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We give a example of non nilpotent faithful representation of a filiform Lie algebra. This gives one counter-example of the conjecture saying that every affine connection on a filiform Lie group is complete. 1. Affine connection on a nilpotent Lie algebra 1.1. Affine connection on nilpotent Lie algebras. Definition 1. Let g be a n-dimensional Lie algebra over R. It is called affine if there is ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(02)00613-4