Nonlinear Lie derivations on upper triangular matrices
Authors:
- 18 September 2008
- journal article
- research article
- Published byย Taylor & Francisย inย Linear and Multilinear Algebra
- Vol.ย 56 ย (6) , 725-730
Abstract
Let M n (๐ธ) and T n (๐ธ) be the algebra of all n ร n matrices and the algebra of all n ร n upper triangular matrices over a commutative unital algebra ๐ธ, respectively. In this note we prove that every nonlinear Lie derivation from T n (๐ธ) into M n (๐ธ) is of the form A โ AT โ TA + A ฯ + ฮพ(A)I n , where T โ M n (๐ธ), ฯ : ๐ธ โ ๐ธ is an additive derivation, ฮพ : T n (๐ธ) โ ๐ธ is a nonlinear map with ฮพ(AB โ BA) = 0 for all A,โB โ T n (๐ธ) and A ฯ is the image of A under ฯ applied entrywise.Keywords
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