Abstract:
Let K be an associative commutative ring with identity and let R be the algebra of lower niltriangular n×n-matrices over K. For n=3 we prove that local automorphisms and Lie ones of the algebra R generate all local Lie automorphisms of the latter. For the case when K is a field and n=4 we describe local automorphisms and local derivations of the algebra R, as well as its local Lie automorphisms.
Keywords:
nilpotent algebra, associated Lie algebra, local automorphism, local derivation.
Citation:
A. P. Elisova, “Local automorphisms of nilpotent algebras of matrices of small orders”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 2, 40–48; Russian Math. (Iz. VUZ), 57:2 (2013), 34–41
\Bibitem{Eli13}
\by A.~P.~Elisova
\paper Local automorphisms of nilpotent algebras of matrices of small orders
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 2
\pages 40--48
\mathnet{http://mi.mathnet.ru/ivm8773}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 2
\pages 34--41
\crossref{https://doi.org/10.3103/S1066369X13020047}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878410028}
Linking options:
https://www.mathnet.ru/eng/ivm8773
https://www.mathnet.ru/eng/ivm/y2013/i2/p40
This publication is cited in the following 4 articles:
Abror Khudoyberdiyev, Doston Jumaniyozov, “Local derivations and automorphisms of nilpotent Lie algebras”, Communications in Algebra, 2024, 1
Karimbergen Kudaybergenov, Tuuelbay Kurbanbaev, Bakhrom Omirov, “Local automorphisms of complex solvable Lie algebras of maximal rank”, Linear and Multilinear Algebra, 2023, 1
I. N. Zotov, V. M. Levchuk, “Nonfinitary algebras and their automorphism groups”, Siberian Math. J., 63:1 (2022), 87–96
Igor N. Zotov, “Local automorphisms of nil-triangular subalgebras of classical lie type Chevalley algebras”, Zhurn. SFU. Ser. Matem. i fiz., 12:5 (2019), 598–605
Citation in format AMSBIB
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