J. C. Benjumea, J. Nunez, A. F. Tenorio, “The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices”, TMF, 152:3 (2007), 419–429; Theoret. and Math. Phys., 152:3 (2007), 1225

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 3, Pages 419–429
DOI: https://doi.org/10.4213/tmf6099 (Mi tmf6099)

This article is cited in 16 scientific papers (total in 16 papers)

The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices

J. C. Benjumea^a, J. Nunez^a, A. F. Tenorio^b

^a University of Seville
^b Universidad Pablo de Olavide

Full-text PDF (400 kB) Citations (16)

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DOI: https://doi.org/10.4213/tmf6099

Abstract: We compute the largest dimension of the Abelian Lie subalgebras contained in the Lie algebra

$\mathfrak g_n$ of

$n\times n$ strictly upper triangular matrices, where

$n\in\mathbb N\setminus\{1\}$ . We do this by proving a conjecture, which we previously advanced, about this dimension. We introduce an algorithm and use it first to study the two simplest particular cases and then to study the general case.

Keywords: nilpotent Lie algebra, maximal Abelian dimension, strictly upper triangular matrix.

Received: 04.01.2007

English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 3, Pages 1225–1233
DOI: https://doi.org/10.1007/s11232-007-0107-z

Bibliographic databases:

Language: Russian

Citation: J. C. Benjumea, J. Nunez, A. F. Tenorio, “The maximal Abelian dimension of linear algebras formed by strictly upper triangular matrices”, TMF, 152:3 (2007), 419–429; Theoret. and Math. Phys., 152:3 (2007), 1225–1233

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Linking options:

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https://doi.org/10.4213/tmf6099

https://www.mathnet.ru/eng/tmf/v152/i3/p419

This publication is cited in the following 16 articles:

Ooms I A., “The Maximal Abelian Dimension of a Lie Algebra, Rentschler'S Property and Milovanov'S Conjecture”, Algebr. Represent. Theory, 23:3 (2020), 963–999
Ceballos M., Nunez J., Tenorio A.F., “Algorithm to compute abelian subalgebras and ideals in Malcev algebras”, Math. Meth. Appl. Sci., 39:16 (2016), 4892–4900
Ceballos M., Nunez J., Tenorio A.F., “Computing Abelian Subalgebras For Linear Algebras of Upper-Triangular Matrices From An Algorithmic Perspective”, Analele Stiint. Univ. Ovidius C., 24:2 (2016), 137–147
Ceballos M., Nunez J., Tenorio A.F., “Algorithmic Procedure To Compute Abelian Subalgebras and Ideals of Maximal Dimension of Leibniz Algebras”, Int. J. Comput. Math., 92:9, SI (2015), 1838–1854
Ceballos M., Nunez J., Tenorio A.F., “Abelian Subalgebras on Lie Algebras”, Commun. Contemp. Math., 17:4 (2015), 1550050
Ceballos M., Nunez J., Tenorio A.F., “Triangular Configurations and Lie Algebras of Strictly Upper-Triangular Matrices”, Appl. Comput. Math., 13:1 (2014), 62–70
Ceballos M., Nunez J., Tenorio A.F., “Combinatorial structures and Lie algebras of upper triangular matrices”, Appl Math Lett, 25:3 (2012), 514–519
Nunez J., Tenorio A.F., “A computational study of a family of nilpotent Lie algebras”, Journal of Supercomputing, 59:1 (2012), 147–155
Ceballos M., Nunez J., Tenorio A.F., “Algorithmic Method to Obtain Abelian Subalgebras and Ideals in Lie Algebras”, Int. J. Comput. Math., 89:10 (2012), 1388–1411
Benjumea J.C., Nunez J., Tenorio A.F., “Maximal Abelian Dimensions in Some Families of Nilpotent Lie Algebras”, Algebr. Represent. Theory, 15:4 (2012), 697–713
Benjumea J.C., Núñez J., Tenorio Á.F., “Computing the law of a family of solvable Lie algebras”, Internat. J. Algebra Comput., 19:3 (2009), 337–345
Ceballos M., Núñez J., Tenorio Á.F., “Algorithm to compute the maximal abelian dimension of Lie algebras”, Computing, 84:3-4 (2009), 231–239
Ceballos M., Nunez J., Tenorio A.F., “Abelian subalgebras in some particular types of Lie algebras”, Nonlinear Analysis-Theory Methods & Applications, 71:12 (2009), E401–E408
Ceballos M., Nunez J., Tenorio A.F., “An Algorithm to Compute Abelian Subalgebras in Linear Algebras of Upper-Triangular Matrices”, Computational Methods in Science and Engineering, AIP Conference Proceedings, 1148, 2009, 53–56
Ceballos M., Nunez J., Tenorio A.F., “Abelian Subalgebras in Low-Dimensional Solvable Lie Algebras”, Recent Advances in Applied Mathematics, Mathematics and Computers in Science and Engineering, 2009, 151–156
Ceballos M., Nunez J., Tenorio A.F., “The computation of abelian subalgebras in the Lie algebra of upper-triangular matrices”, An. Ştiinţ. Univ. “Ovidius” Constanţa Ser. Mat., 16:1 (2008), 59–66

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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