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Mat. Zametki, 2020, Volume 107, Issue 1, Pages 23–31 (Mi mz11585)  

Computational Experiments with Nilpotent Lie Algebras

V. V. Gorbatsevich


Abstract: Results of computer experiments on the study of properties of generic Lie subalgebras with two generators in the Lie algebra of nilpotent matrices whose order does not exceed 10 are presented. The calculations carried out have made it possible to formulate several statements (so-called virtual theorems) on properties of the Lie subalgebras in question. The dimensions of the lower and upper central series and of the series of commutator subalgebras and the characteristic nilpotency property of the Lie subalgebras constructed here and of generic Lie subalgebras of codimension 1 in these Lie subalgebras are studied.

Keywords: nilpotent Lie algebra, matrix Lie algebra, characteristically nilpotent Lie algebra, filiform Lie algebra.

DOI: https://doi.org/10.4213/mzm11585

Full text: PDF file (412 kB)
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English version:
Mathematical Notes, 2020, 107:1, 20–26

Bibliographic databases:

UDC: 512.554.3
Received: 15.03.2017
Revised: 22.03.2017

Citation: V. V. Gorbatsevich, “Computational Experiments with Nilpotent Lie Algebras”, Mat. Zametki, 107:1 (2020), 23–31; Math. Notes, 107:1 (2020), 20–26

Citation in format AMSBIB
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