English
Related papers

Related papers: Derivations on four dimensional genetic Volterra a…

200 papers

This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a…

Rings and Algebras · Mathematics 2024-01-11 Qingyan Wu , Shoulan Gao , Dong Liu , Chang Ye

In the present paper 2-local derivations on various algebras of infinite dimensional matrix-valued functions on a compact are considered. It is proved that every 2-local derivation on such algebra is a derivation. Also we explain that the…

Operator Algebras · Mathematics 2015-09-21 Shavkat Ayupov , Farhodjon Arzikulov

This article investigates the recently introduced three-parameter generalized quaternion algebra (3PGQ), denoted here as $\mathbb{K}_{\lambda_1,\lambda_2,\lambda_3}$ . Our analysis is structured in three parts. First, we demonstrate that…

Rings and Algebras · Mathematics 2025-11-25 Hassan Oubba

In this paper, we prove that every 2-local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++} $ is a derivation for all $n=1,2,\cdots,\infty$. As a consequence we obtain that every 2-local derivation on any centerless generalized…

Rings and Algebras · Mathematics 2020-03-31 Yueqiang Zhao , Yang Chen , Kaiming Zhao

In a first result we prove that every continuous local triple derivation on a JB$^*$-triple is a triple derivation. We also give an automatic continuity result, that is, we show that local triple derivations on a JB$^*$-triple are…

Functional Analysis · Mathematics 2017-05-17 María Burgos , Francisco J. Fernández-Polo , Antonio M. Peralta

In the present paper we study local and 2-local derivations of locally finite split simple Lie algebras. Namely, we show that every local and 2-local derivation on such Lie algebra is a derivation.

Rings and Algebras · Mathematics 2020-05-26 Shavkat Ayupov , Karimbergen Kudaybergenov , Bakhtiyor Yusupov

In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras…

Rings and Algebras · Mathematics 2019-04-24 Izzat Qaralleh , Farrukh Mukhamedov

In the present paper we prove that every 2-local derivation on a semi-finite von Neumann algebra is a derivation.

Operator Algebras · Mathematics 2014-09-22 Shavkat Ayupov , Farkhad Arzikulov

In the present paper, we prove that a local derivation on the octonion (Cayley) algebra $\mathbb{O}$ over an arbitrary field, satisfying some conditions is a derivation, and every 2-local derivation on $\mathbb{O}$ is a Jordan derivation.

Rings and Algebras · Mathematics 2023-05-24 F. N. Arzikulov , I. A. Karimjanov , S. Uguz

Using the first cohomology from the mirror Heisenberg-Virasoro algebra to the twisted Heisenberg algebra (as the mirror Heisenberg-Virasoro algebra-module), in this paper we determined the derivations on the mirror Heisenberg-Virasoro…

Rings and Algebras · Mathematics 2023-06-27 Xuelian Guo , Liming Tang

This paper is devoted to the study of local and 2-local derivations of nullfiliform, filiform and naturally graded quasi-filiform associative algebras. We prove that these algebras as a rule admit local derivations which are not…

Rings and Algebras · Mathematics 2023-06-27 K. K. Abdurasulov , Sh. A. Ayupov , B. B. Yusupov

In the present paper we prove that every additive (not necessarily homogenous) local inner derivation on the algebra of matrices over an arbitrary field is an inner derivation, and every local inner derivation on the ring of matrices over a…

Rings and Algebras · Mathematics 2019-01-28 Sh. Ayupov , F. Arzikulov

R.V. Kadison defined the notion of local derivation on an algebra and proved that every continuous local derivation on a von Neumann algebra is a derivation (Kadison 1990). We provide the analogous result in the setting of Jordan triples.

Operator Algebras · Mathematics 2016-10-20 Michael Mackey

Given a finite-dimensional complex simple $\omega$-Lie algebras $\mathfrak{}$ over $\mathbb{C}$. We prove that every local ,$2-$local derivation is a derivation and every local (resp. 2-local) automorphisms are automorphisms or an…

Rings and Algebras · Mathematics 2025-05-02 Hassan Oubba

In this work we investigate the derivations of $n-$dimensional complex evolution algebras, depending on the rank of the appropriate matrices. For evolution algebra with non-singular matrices we prove that the space of derivations is zero.…

Commutative Algebra · Mathematics 2018-05-01 L. M. Camacho , J. R. Gómez , B. A. Omirov , R. M. Turdibaev

We present a general framework for calculating the Volterra-type convolution of polynomials from an arbitrary polynomial sequence $\{P_k(x)\}_{k \geqslant 0}$ with $\deg P_k(x) = k$. Based on this framework, series representations for the…

Classical Analysis and ODEs · Mathematics 2018-04-27 Ana F. Loureiro , Kuan Xu

The paper is devoted to 2-local derivations on matrix algebras over commutative regular algebras. We give necessary and sufficient conditions on a commutative regular algebra to admit 2-local derivations which are not derivations. We prove…

Operator Algebras · Mathematics 2013-04-12 Sh. A. Ayupov , K. K. Kudaybergenov , A. K. Alauadinov

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose the dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals,…

Rings and Algebras · Mathematics 2019-11-12 Sh. A. Ayupov , A. Kh. Khudoyberdiyev , B. B. Yusupov

Let $\mathcal{H}$ be a separable Hilbert space and $\mathcal{L}_{0}\subset B(\mathcal{H})$ a complete reflexive lattice. Let $\mathscr{K}$ be the direct sum of $n_0$ copies of $\mathcal{H}$ ($n_{0}\in\mathbb{N}$ and $n_0\geq 2$) or the…

Operator Algebras · Mathematics 2025-01-08 Hongjie Chen , Liguang Wang , Zhujun Yang

The paper is devoted to 2-local derivations and 2-local automorphisms on the algebra $B(H)$ of all bounded linear operators on a Hilbert space $H.$ We prove that every 2-local derivation on $B(H)$ is a derivation. A similar result is…

Operator Algebras · Mathematics 2011-11-15 Sh. A. Ayupov , K. K. Kudaybergenov