Local automorphisms of nilpotent algebras of matrices of small orders

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 automorphisms of the algebra R generate all its local Lie automorphisms. For the case when K is a field and n = 4, we describe local automorphisms, local derivations, and local Lie automorphisms of the algebra R.

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