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

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 />

scholarly journals Characterizations of Lie derivations of triangular algebras

2011 ◽  
Vol 435 (5) ◽  
pp. 1137-1146 ◽  
Author(s):  
Peisheng Ji ◽  
Weiqing Qi
Keyword(s):  
Triangular Algebras ◽  
Lie Derivations

scholarly journals Lie Derivations on Trivial Extension Algebras

2017 ◽  
Vol 31 (1) ◽  
pp. 141-153 ◽  
Author(s):  
Amir Hosein Mokhtari ◽  
Fahimeh Moafian ◽  
Hamid Reza Ebrahimi Vishki
Keyword(s):  
Trivial Extension ◽  
Lie Derivation ◽  
Trivial Extension Algebra ◽  
Triangular Algebras ◽  
Extension Algebra ◽  
Lie Derivations

Abstract In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.

Nonlinear generalized Lie derivations on triangular algebras

2016 ◽  
Vol 65 (6) ◽  
pp. 1158-1170 ◽  
Author(s):  
Xiuhai Fei ◽  
Jianhua Zhang
Keyword(s):  
Triangular Algebras ◽  
Lie Derivations

A fixed point approach to the stability of sextic Lie *-derivations

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4933-4944
Author(s):  
Dongseung Kang ◽  
Heejeong Koh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
General Solution ◽  
Single Case ◽  
Fixed Point Method ◽  
Point Method ◽  
Fixed Point Approach ◽  
The Stability ◽  
The Given ◽  
Lie Derivations

We obtain a general solution of the sextic functional equation f (ax+by)+ f (ax-by)+ f (bx+ay)+ f (bx-ay) = (ab)2(a2 + b2)[f(x+y)+f(x-y)] + 2(a2-b2)(a4-b4)[f(x)+f(y)] and investigate the stability of sextic Lie *-derivations associated with the given functional equation via fixed point method. Also, we present a counterexample for a single case.

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