Lie σ-derivations of triangular algebras

2020 ◽  
pp. 1-18
Author(s):  
Dominik Benkovič
Keyword(s):  
Triangular Algebras

scholarly journals Nonlinear Lie derivations of triangular algebras

2010 ◽  
Vol 432 (11) ◽  
pp. 2953-2960 ◽  
Author(s):  
Weiyan Yu ◽  
Jianhua Zhang
Keyword(s):  
Triangular Algebras ◽  
Lie Derivations

Nonlinear Lie higher derivations on triangular algebras

2012 ◽  
Vol 60 (8) ◽  
pp. 979-994 ◽  
Author(s):  
Zhankui Xiao ◽  
Feng Wei
Keyword(s):  
Triangular Algebras

scholarly journals Generalized Higher Derivations on Lie Ideals of Triangular Algebras

2017 ◽  
Vol 25 (1) ◽  
pp. 35-53
Author(s):  
Mohammad Ashraf ◽  
Nazia Parveen ◽  
Bilal Ahmad Wani
Keyword(s):  
Commutative Ring ◽  
Lie Ideal ◽  
Additive Subgroup ◽  
Triangular Algebra ◽  
Higher Derivation ◽  
Square Closed Lie Ideal ◽  
Triangular Algebras

Abstract Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.

Triangular Algebras

1988 ◽  
pp. 447-498 ◽  
Author(s):  
Murray Gerstenhaber ◽  
Samuel D. Schack
Keyword(s):  
Triangular Algebras

scholarly journals Zero-Sum Coefficient Derivations in Three Variables of Triangular Algebras

2016 ◽  
Vol 8 (5) ◽  
pp. 37
Author(s):  
Youngsoo Kim ◽  
Byunghoon Lee
Keyword(s):  
Standard Form ◽  
Sufficient Conditions ◽  
Multilinear Polynomial ◽  
Triangular Algebra ◽  
Triangular Algebras ◽  
Zero Sum ◽  
Lie Derivations

Under mild assumptions Benkovi\v{c} showed that an $f$-derivation of a triangular algebra is a derivation when the sum of the coefficients of the multilinear polynomial $f$ is nonzero. We investigate the structure of $f$-derivations of triangular algebras when $f$ is of degree 3 and the coefficient sum is zero. The zero-sum coeffient derivations include Lie derivations (degree 2) and Lie triple derivations (degree 3), which have been previously shown to be not necessarily derivations but in standard form, i.e., the sum of a derivation and a central map. In this paper, we present sufficient conditions on the coefficients of $f$ to ensure that any $f$-derivations are derivations or are in standard form.<br /><br />

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