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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. Benjumeaa, J. Nuneza, A. F. Tenoriob

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
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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