This article is cited in 4 papers

Local automorphisms of nilpotent algebras of matrices of small orders

A. P. Elisova

Chair of Algebra and Mathematical Logic, Siberian Federal University, Krasnoyarsk, Russia

Abstract: Let $K$ be an associative commutative ring with identity and let $R$ be the algebra of lower niltriangular $n\times n$-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.

UDC: 512.554

Received: 20.01.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 34–41

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