REPRESENTING FILIFORM LIE ALGEBRAS MINIMALLY AND FAITHFULLY BY STRICTLY UPPER-TRIANGULAR MATRICES
2013 ◽
Vol 12
(04)
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pp. 1250196
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Keyword(s):
In this paper, we compute minimal faithful representations of filiform Lie algebras by means of strictly upper-triangular matrices. To obtain such representations, we use nilpotent Lie algebras [Formula: see text]n, of n × n strictly upper-triangular matrices, because any given (filiform) nilpotent Lie algebra [Formula: see text] admits a Lie-algebra isomorphism with a subalgebra of [Formula: see text]n for some n ∈ ℕ\{1}. In this sense, we search for the lowest natural integer n such that the Lie algebra [Formula: see text]n contains the filiform Lie algebra [Formula: see text] as a subalgebra. Additionally, we give a representative of each representation.
2014 ◽
Vol 13
(04)
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pp. 1350144
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Keyword(s):
2006 ◽
Vol 54
(5)
◽
pp. 369-377
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Keyword(s):
2009 ◽
Vol 19
(03)
◽
pp. 337-345
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Keyword(s):
2019 ◽
Vol 19
(01)
◽
pp. 2050012
Keyword(s):
1982 ◽
Vol 34
(6)
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pp. 1215-1239
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2002 ◽
Keyword(s):
2017 ◽
Vol 27
(07)
◽
pp. 953-972