Complex filiform Lie algebras of dimension 11

Boza, L.; Fedriani, Eugenio M.; Núñez, Juan

doi:10.1016/s0096-3003(02)00280-1

Cited by 10 publications

(11 citation statements)

References 9 publications

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“…In 1991, J.R. G ómez classified those of dimension 9 in his Ph. D. Thesis, later published by F.J. Echarte and himself in [84], and L. Boza, F.J. Echarte and J. N ú ñez [39] those of dimension 10 in 1994. Later, J.R. G ómez, A. Jiménez and Y.B.…”

Section: Nilpotent Lie Algebras: Classificationmentioning

confidence: 99%

“…Regarding the explicit lists, L. Boza, E.M. Fedriani and J. N ú ñez [40] got in 1998 the classification of complex filiform Lie algebras of dimension 12, and also showed in 2003 ( [42]) an explicit classification of such algebras of dimension 11, in a different way as the one used in [110]. Although [41] supplied a method valid for every dimension over the complex field, the involved computations are too hard to be nowadays tacked successfully.…”

Section: Nilpotent Lie Algebras: Classificationmentioning

confidence: 99%

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The trascendence of Kac-Moody algebras

Fernández-Ternero

Valdés

2021

Filomat

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With the main objective that it can be consulted by all researchers, mainly young people, interested in the study of the Kac-Moody algebras and their applications, this paper aims to present the past and present state-of-the-art developments and results on these algebras at various levels of analysis and fields of application in different disciplines. Indeed, lot of references in the literature on these algebras are analyzed and a study of the most relevant topics regarding them is shown.

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Section: Nilpotent Lie Algebras: Classificationmentioning

confidence: 99%

Section: Nilpotent Lie Algebras: Classificationmentioning

confidence: 99%

The trascendence of Kac-Moody algebras

Fernández-Ternero

Valdés

2021

Filomat

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“…Gómez et al [17] classified the symplectic filiform Lie algebras that are not two-to-two symplectic-isomorphic of dimensions less than or equal to 10 in 2001. Higher dimensions were tackled by Boza et al [18] and Echarte et al [19,20] in the last ten years. The more the dimension increases, the more and more complex is the determination of exhaustive lists of Lie algebras, so new computation methodologies are a present field of research [21][22][23].…”

Section: State Of the Artmentioning

confidence: 99%

Symbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine

Pérez

Jiménez

2015

Symmetry

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This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in traditional mechanical dynamic problems and current scientific disciplines. The conditions of being quasi-filiform and nilpotent are applied carefully and in several stages, and appropriate changes of the basis are achieved in an iterative and interactive process of simplification. This has been implemented by means of the development of more than thirty Maple modules. The process has led from the first family formulation, with 64 parameters and 215 constraints, to a family of 16 parameters and 17 constraints. This structure theorem permits the exhaustive classification of the quasi-filiform nilpotent Lie algebras of dimension nine with current computational methodologies.

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“…They were introduced formally by Vergne [21,22] in the late 1960s, although Umlauf had already used them as an example in his thesis [19]. The distribution into isomorphism classes of n-dimensional filiform Lie algebras over the complex field is known for n ≤ 12 [6,11], even if it is only known for nilpotent Lie algebras over the complex field of dimension n ≤ 7 [4]. More recently, some authors have dealt with the classification of n-dimensional nilpotent Lie algebras over finite fields F p = Z/pZ.…”

Section: Introductionmentioning

confidence: 99%

Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields

2016

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Since the introduction of the concept of isotopism of algebras by Albert in 1942, a prolific literature on the subject has been developed for distinct types of algebras. Nevertheless, there barely exists any result on the problem of distributing Lie algebras into isotopism classes. The current paper is a first step to deal with such a problem. Specifically, we define a new series of isotopism invariants and we determine explicitly the distribution into isotopism classes of n-dimensional filiform Lie algebras, for n ≤ 7. We also deal with the distribution of such algebras into isomorphism classes, for which we confirm some known results and we prove that there exist p + 8 isomorphism classes of seven-dimensional filiform Lie algebras over the finite field F p if p = 2.

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Complex filiform Lie algebras of dimension 11

Cited by 10 publications

References 9 publications

The trascendence of Kac-Moody algebras

The trascendence of Kac-Moody algebras

Symbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine

Isomorphism and Isotopism Classes of Filiform Lie Algebras of Dimension up to Seven Over Finite Fields

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