Quaestiones Mathematicae, ISSN 1607-3606, 08/2019, Volume 42, Issue 7, pp. 857 - 884

Let be a standard operator algebra on an infinite dimensional complex Hilbert space containing identity operator I. In this paper it is shown that if is closed...

16W25 | 46K15 | 47B47 | multiplicative ∗-Lie triple higher derivation | Multiplicative ∗-Lie derivation | standard operator algebra | MATHEMATICS | MAPS | PRODUCT | Multiplicative -Lie derivation | MAPPINGS | multiplicative -Lie triple higher derivation

16W25 | 46K15 | 47B47 | multiplicative ∗-Lie triple higher derivation | Multiplicative ∗-Lie derivation | standard operator algebra | MATHEMATICS | MAPS | PRODUCT | Multiplicative -Lie derivation | MAPPINGS | multiplicative -Lie triple higher derivation

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2019, Volume 47, Issue 5, pp. 1841 - 1852

Let be a 2-torsion free commutative ring with unity, X a locally finite preordered set and the incidence algebra of X over . If X consists of a finite number...

Lie triple derivation | 06A11 | Derivation | Primary 16W25 | Secondary 16W10 | 47L35 | incidence algebra | Incidence

Lie triple derivation | 06A11 | Derivation | Primary 16W25 | Secondary 16W10 | 47L35 | incidence algebra | Incidence

Journal Article

Journal of Algebra, ISSN 0021-8693, 02/2014, Volume 399, pp. 960 - 977

We introduce the notion of Banach Jordan triple modules and determine the precise conditions under which every derivation from a JB⁎-triple E into a Banach...

Triple derivation | [formula omitted]-algebra | Automatic continuity | Jordan triple module | Jordan triple | Derivation | [formula omitted]-triple | Jordan derivation | Jordan algebra | triple | algebra | HOMOMORPHISMS | JB-algebra | SPACES | BANACH ALGEBRAS | DECOMPOSITION | LIE | JB-triple | MATHEMATICS | KAPLANSKY THEOREM | STAR-TRIPLES | REAL | OPERATOR ALGEBRAS | JORDAN DERIVATIONS | C-algebra | Algebra

Triple derivation | [formula omitted]-algebra | Automatic continuity | Jordan triple module | Jordan triple | Derivation | [formula omitted]-triple | Jordan derivation | Jordan algebra | triple | algebra | HOMOMORPHISMS | JB-algebra | SPACES | BANACH ALGEBRAS | DECOMPOSITION | LIE | JB-triple | MATHEMATICS | KAPLANSKY THEOREM | STAR-TRIPLES | REAL | OPERATOR ALGEBRAS | JORDAN DERIVATIONS | C-algebra | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2017, Volume 45, Issue 10, pp. 4380 - 4395

Let ℛ be a commutative ring with identity and let = Tri( ,ℳ,ℬ) be a triangular algebra consisting of unital algebras ,ℬ over ℛ and an ( ,ℬ)-bimodule ℳ which...

16W25 | Lie triple derivation | 15A78 | Generalized Lie triple derivation | Triangular algebra | MATHEMATICS | Derivation | Mathematical analysis | Algebra

16W25 | Lie triple derivation | 15A78 | Generalized Lie triple derivation | Triangular algebra | MATHEMATICS | Derivation | Mathematical analysis | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 11/2019, Volume 47, Issue 11, pp. 4791 - 4796

Let be a unite prime *-algebra containing a non-trivial projection, and be a nonlinear mixed Lie triple derivation. Then is an additive *-derivation.

algebra | Prime | 47B47 | mixed Lie triple derivation | 16N60 | MATHEMATICS | Derivation

algebra | Prime | 47B47 | mixed Lie triple derivation | 16N60 | MATHEMATICS | Derivation

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 4/2018, Volume 41, Issue 2, pp. 637 - 656

In this paper, we give some properties of the generalized derivation algebra $$\mathrm{GDer}(T)$$ GDer(T) of a Hom–Lie triple systems T. In particular, we...

17A75 | 17B30 | Hom–Lie triple systems | Mathematics, general | Generalized derivations | 17B70 | Mathematics | Centroids | Applications of Mathematics | MATHEMATICS | ALGEBRAS | COHOMOLOGY | Hom-Lie triple systems | EXTENSIONS | NAMBU | DEFORMATIONS | SUPERALGEBRAS | Embedded systems

17A75 | 17B30 | Hom–Lie triple systems | Mathematics, general | Generalized derivations | 17B70 | Mathematics | Centroids | Applications of Mathematics | MATHEMATICS | ALGEBRAS | COHOMOLOGY | Hom-Lie triple systems | EXTENSIONS | NAMBU | DEFORMATIONS | SUPERALGEBRAS | Embedded systems

Journal Article

Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 9/2018, Volume 39, Issue 5, pp. 817 - 828

Let $$\mathcal{A}$$ A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ : $$\mathcal{A}$$ A →...

47B47 | von Neumann algebras | Mathematics, general | 16W25 | Mathematics | Applications of Mathematics | Derivations | Lie triple derivations | MATHEMATICS | CHARACTERIZING HOMOMORPHISMS | OPERATOR-ALGEBRAS | NEST-ALGEBRAS | IDEMPOTENTS | Algebra

47B47 | von Neumann algebras | Mathematics, general | 16W25 | Mathematics | Applications of Mathematics | Derivations | Lie triple derivations | MATHEMATICS | CHARACTERIZING HOMOMORPHISMS | OPERATOR-ALGEBRAS | NEST-ALGEBRAS | IDEMPOTENTS | Algebra

Journal Article

数学学报：英文版, ISSN 1439-8516, 2016, Volume 32, Issue 7, pp. 821 - 830

Abstract Let A be a factor. For A, B ∈4, define by [A, B]. = AB- BA＊ the skew Lie product of A and B. In this article, it is proved that a map φ： A- A...

非线性 | 添加剂 | 三倍数 | 传递因数 | 47B49 | Skew Lie triple derivation | Mathematics, general | Mathematics | derivation | factor | 46L10 | VON-NEUMANN-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCT | JORDAN ASTERISK-DERIVATIONS | B(H) | QUADRATIC FUNCTIONALS | Yuan (China) | Studies | Theorems | Mathematical models | Algebra | Derivation | Mathematical analysis | Nonlinearity

非线性 | 添加剂 | 三倍数 | 传递因数 | 47B49 | Skew Lie triple derivation | Mathematics, general | Mathematics | derivation | factor | 46L10 | VON-NEUMANN-ALGEBRAS | MATHEMATICS | MATHEMATICS, APPLIED | PRODUCT | JORDAN ASTERISK-DERIVATIONS | B(H) | QUADRATIC FUNCTIONALS | Yuan (China) | Studies | Theorems | Mathematical models | Algebra | Derivation | Mathematical analysis | Nonlinearity

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 09/2012, Volume 437, Issue 5, pp. 1234 - 1249

Let R be a commutative ring with identity, A,B be unital algebras over R and M be a unital (A,B)-bimodule, which is faithful as a left A-module and also as a...

Lie triple derivation | Triangular algebra | MATHEMATICS, APPLIED | NEUMANN ALGEBRAS | NEST-ALGEBRAS | RINGS | Employee motivation | Algebra

Lie triple derivation | Triangular algebra | MATHEMATICS, APPLIED | NEUMANN ALGEBRAS | NEST-ALGEBRAS | RINGS | Employee motivation | Algebra

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 4/2018, Volume 44, Issue 2, pp. 513 - 530

Let $${\mathcal {R}}$$ R be a commutative ring with unity. A triangular algebra is an algebra of the form $${\mathfrak {A}} = \left[ \begin{array}{cc}...

Generalized higher derivation | 15A78 | Generalized Lie triple higher derivation | Mathematics, general | 16W25 | Mathematics | Triangular algebra | MATHEMATICS | OPERATOR-ALGEBRAS

Generalized higher derivation | 15A78 | Generalized Lie triple higher derivation | Mathematics, general | 16W25 | Mathematics | Triangular algebra | MATHEMATICS | OPERATOR-ALGEBRAS

Journal Article

Indagationes Mathematicae, ISSN 0019-3577, 04/2017, Volume 28, Issue 2, pp. 436 - 445

In this paper, we study triple derivations and triple homomorphisms of perfect Lie superalgebras over a commutative ring R. It is proved that, if the base ring...

Triple derivations | Perfect Lie superalgebras | Enveloping Lie superalgebras | Triple homomorphisms | VON-NEUMANN-ALGEBRAS | MATHEMATICS | RINGS | Algebra | Mathematics - Rings and Algebras

Triple derivations | Perfect Lie superalgebras | Enveloping Lie superalgebras | Triple homomorphisms | VON-NEUMANN-ALGEBRAS | MATHEMATICS | RINGS | Algebra | Mathematics - Rings and Algebras

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 01/2011, Volume 434, Issue 1, pp. 259 - 284

Let R be a 2-torsion free commutative ring with identity, A,B be unital algebras over R and M be a unital (A,B)-bimodule, which is faithful as a left A-module...

Jordan [formula omitted]-derivation | Jordan triple [formula omitted]-derivation | [formula omitted]-Derivation | Generalized Jordan [formula omitted]-derivation | Triangular algebra | Generalized Jordan (α,β)-derivation | (α,β)-Derivation | Jordan triple (α,β)-derivation | Jordan (α,β)-derivation | MATHEMATICS, APPLIED | (alpha, beta)-derivation | OPERATOR-ALGEBRAS | NEST-ALGEBRAS | Jordan triple (alpha, beta)-derivation | Jordan (alpha, beta)-derivation | SEMIPRIME RINGS | MAPS | BIDERIVATIONS | GROWTH | Generalized Jordan (alpha, beta)-derivation | MATRIX-RINGS | LIE DERIVATIONS | IDEMPOTENTS

Jordan [formula omitted]-derivation | Jordan triple [formula omitted]-derivation | [formula omitted]-Derivation | Generalized Jordan [formula omitted]-derivation | Triangular algebra | Generalized Jordan (α,β)-derivation | (α,β)-Derivation | Jordan triple (α,β)-derivation | Jordan (α,β)-derivation | MATHEMATICS, APPLIED | (alpha, beta)-derivation | OPERATOR-ALGEBRAS | NEST-ALGEBRAS | Jordan triple (alpha, beta)-derivation | Jordan (alpha, beta)-derivation | SEMIPRIME RINGS | MAPS | BIDERIVATIONS | GROWTH | Generalized Jordan (alpha, beta)-derivation | MATRIX-RINGS | LIE DERIVATIONS | IDEMPOTENTS

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 10/2012, Volume 60, Issue 10, pp. 1155 - 1164

Let be a triangular algebra over a 2-torsion free commutative ring R. In this article, under some mild conditions on , we prove that if δ: → is a nonlinear...

16W25 | 47B49 | triangular algebra | nonlinear Lie triple derivation | additive derivation | MATHEMATICS | NEST-ALGEBRAS | Algebra | Additives | Images | Derivation | Nonlinearity | Mapping | Rings (mathematics)

16W25 | 47B49 | triangular algebra | nonlinear Lie triple derivation | additive derivation | MATHEMATICS | NEST-ALGEBRAS | Algebra | Additives | Images | Derivation | Nonlinearity | Mapping | Rings (mathematics)

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 01/2015, Volume 63, Issue 1, pp. 141 - 165

Let be a unital algebra with a nontrivial idempotent over a unital commutative ring . We show that under suitable assumptions, every Lie triple derivation on...

Lie derivation | Lie triple derivation | triangular algebra | unital algebra | 16W25 | derivation | Jordan derivation | MATHEMATICS | TRIANGULAR ALGEBRAS | COMMUTING MAPS | NEST-ALGEBRAS | GENERALIZED MATRIX ALGEBRAS | Algebra | Matrix algebra | Mathematical analysis | Images | Derivation | Mapping | Rings (mathematics)

Lie derivation | Lie triple derivation | triangular algebra | unital algebra | 16W25 | derivation | Jordan derivation | MATHEMATICS | TRIANGULAR ALGEBRAS | COMMUTING MAPS | NEST-ALGEBRAS | GENERALIZED MATRIX ALGEBRAS | Algebra | Matrix algebra | Mathematical analysis | Images | Derivation | Mapping | Rings (mathematics)

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 03/2011, Volume 59, Issue 3, pp. 237 - 247

Let be a complex semisimple Lie algebra, be a Borel subalgebra of and denote the maximal nilpotent subalgebra of . In this article, we prove that every...

block diagonal map | 17B40 | 17B20 | homothety | Borel subalgebra | maximal nilpotent subalgebra | generalized Lie triple derivation | Maximal nilpotent subalgebra | Homothety | Generalized lie triple derivation | Block diagonal map | MATHEMATICS | COMMUTATIVE RING | ALGEBRAS | TRIANGULAR MATRICES

block diagonal map | 17B40 | 17B20 | homothety | Borel subalgebra | maximal nilpotent subalgebra | generalized Lie triple derivation | Maximal nilpotent subalgebra | Homothety | Generalized lie triple derivation | Block diagonal map | MATHEMATICS | COMMUTATIVE RING | ALGEBRAS | TRIANGULAR MATRICES

Journal Article

Communications in Algebra, ISSN 0092-7872, 05/2013, Volume 41, Issue 5, pp. 1647 - 1654

We investigate the triple derivation algebras of Lie algebras. It is proved that, if the base ring contains , L is a perfect Lie algebra with zero center, then...

Triple derivation | Derivation | Lie algebra | MATHEMATICS | RINGS | Algebra

Triple derivation | Derivation | Lie algebra | MATHEMATICS | RINGS | Algebra

Journal Article

Journal of Computational Analysis and Applications, ISSN 1521-1398, 2017, Volume 22, Issue 1, pp. 45 - 51

We prove the Hyers-Ulam stability of ternary Jordan bi-derivations on Banach Lie triple systems associated to the Cauchy functional equation.

Bi-additive mapping | Hyers-ulam stability | Lie triple system | Ternary Jordan bi-derivation | MATHEMATICS, APPLIED | ALGEBRAS | ternary Jordan bi-derivation | STABILITY | SUPERSTABILITY | COMPUTER SCIENCE, THEORY & METHODS | Hyers-Ulam stability | bi-additive mapping | ASTERISK-HOMOMORPHISMS | FUNCTIONAL-EQUATION

Bi-additive mapping | Hyers-ulam stability | Lie triple system | Ternary Jordan bi-derivation | MATHEMATICS, APPLIED | ALGEBRAS | ternary Jordan bi-derivation | STABILITY | SUPERSTABILITY | COMPUTER SCIENCE, THEORY & METHODS | Hyers-Ulam stability | bi-additive mapping | ASTERISK-HOMOMORPHISMS | FUNCTIONAL-EQUATION

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 6/2013, Volume 52, Issue 6, pp. 2118 - 2127

Let be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space with , and the associated CSL...

Lie triple derivation | Theoretical, Mathematical and Computational Physics | CSL algebra | Derivation | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | Algebra

Lie triple derivation | Theoretical, Mathematical and Computational Physics | CSL algebra | Derivation | Quantum Physics | Physics, general | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | Algebra

Journal Article

Czechoslovak Mathematical Journal, ISSN 0011-4642, 6/2010, Volume 60, Issue 2, pp. 541 - 547

Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that...

θ -derivation | Mathematics | Ordinary Differential Equations | Jordan triple ( φ, ψ )-derivation | Convex and Discrete Geometry | Analysis | Lie triple system | Mathematics, general | 16W25 | Jordan triple θ -derivation | Mathematical Modeling and Industrial Mathematics | ( φ, ψ )-derivation | 17A40 | Jordan triple (φ, ψ)-derivation | θ-derivation | (φ, ψ)-derivation | Jordan triple θ-derivation | MATHEMATICS | SEMIPRIME RINGS | (phi, psi)-derivation | Jordan triple (phi, psi)-derivation | Jordan triple theta-derivation | theta-derivation

θ -derivation | Mathematics | Ordinary Differential Equations | Jordan triple ( φ, ψ )-derivation | Convex and Discrete Geometry | Analysis | Lie triple system | Mathematics, general | 16W25 | Jordan triple θ -derivation | Mathematical Modeling and Industrial Mathematics | ( φ, ψ )-derivation | 17A40 | Jordan triple (φ, ψ)-derivation | θ-derivation | (φ, ψ)-derivation | Jordan triple θ-derivation | MATHEMATICS | SEMIPRIME RINGS | (phi, psi)-derivation | Jordan triple (phi, psi)-derivation | Jordan triple theta-derivation | theta-derivation

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 06/2012, Volume 436, Issue 11, pp. 4223 - 4240

We introduce the notion of a multiplicative Lie n-derivation of a ring, generalizing the notion of a Lie (triple) derivation. The main goal of the paper is to...

Lie derivation | Lie triple derivation | Nest algebra | Derivation | Upper triangular matrix ring | Multiplicative Lie n-derivation | Triangular ring | MATHEMATICS, APPLIED | TRIPLE DERIVATIONS | BANACH-ALGEBRAS | NEST-ALGEBRAS | COMMUTING TRACES | MAPS | MAPPINGS | Algebra

Lie derivation | Lie triple derivation | Nest algebra | Derivation | Upper triangular matrix ring | Multiplicative Lie n-derivation | Triangular ring | MATHEMATICS, APPLIED | TRIPLE DERIVATIONS | BANACH-ALGEBRAS | NEST-ALGEBRAS | COMMUTING TRACES | MAPS | MAPPINGS | Algebra

Journal Article

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