60 citations · 262 across the 47 of their papers we have counts for
16 papers · 1 filter
Local and -local automorphisms of Cayley algebras
Shavkat Ayupov, Alberto Elduque, Karimbergen Kudaybergenov
The present paper is devoted to the description of local and 2-local automorphisms on Cayley algebras over an arbitrary field . Given a Cayley algebra wit…
Local and -local derivations of Cayley algebras
Shavkat Ayupov, Alberto Elduque, Karimbergen Kudaybergenov
The present paper is devoted to the description of local and -local derivations on Cayley algebras over an arbitrary field . Given a Cayley algebra wit…
Local and 2-local derivations of Locally simple Lie algebras
Shavkat Ayupov, Karimbergen Kudaybergenov, Bakhtiyor Yusupov
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…
Local and 2-local derivations of solvable Leibniz algebras
Sh. A. Ayupov, A. Kh. Khudoyberdiyev, B. B. Yusupov
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…
Local derivations on associative and Jordan matrix algebras
Sh. Ayupov, F. Arzikulov
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…
2-local derivations on infinite-dimensional Lie algebras
Shavkat Ayupov, Baxtiyor Yusupov
The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations on the Wit…
Description of 2-local derivations on some Lie rings of skew-adjoint matrices
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper we prove that every 2-local inner derivation on the Lie ring of skew-symmetric matrices over a commutative ring is an inner derivation. We also apply our techn…
Local automorphisms on finite-dimensional Lie and Leibniz algebras
Shavkat Ayupov, Karimbergen Kudaybergenov
We prove that a linear mapping on the algebra \(\mathfrak{sl}_n\) of all trace zero complex matrices is a local automorphism if and only if it is an automorphism or an anti-automor…
Semisimple Leibniz algebras and their derivations and automorphisms
Shavkat Ayupov, Karimbergen Kudaybergenov, Bakhrom Omirov +1
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
Two-Local derivations on associative and Jordan matrix rings over commutative rings
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper we prove that every 2-local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has…
Local and 2-local derivations and automorphisms on simple Leibniz algebras
Shavkat Ayupov, Karimbergen Kudaybergenov, Bakhrom Omirov
The present paper is devoted to local and 2-local derivations and automorphism of complex finite-dimensional simple Leibniz algebras. We prove that all local derivations and 2-loca…
-local automorphisms on finite-dimensional Lie algebras
Shavkat Ayupov, Karimbergen Kudaybergenov
We prove that every -local automorphism on a finite-dimensional semi-simple Lie algebra over an algebraically closed field of characteristic zero is an automorphis…
Local derivations on finite-dimensional Lie algebras
Shavkat Ayupov, Karimbergen Kudaybergenov
We prove that every local derivation on a finite-dimensional semisimple Lie algebra over an algebraically closed field of characteristic zero is a derivation. We also give examples…
2-Local derivations on matrix rings over associative rings
Shavkat Ayupov, Farhodjon Arzikulov
In the present paper it is proved that every inner 2-local derivation on the matrix ring of matrices over a commutative associative ring is an inner de…
Cartan Subalgebras of Leibniz -Algebras
S. Albeverio, Sh. A. Ayupov, B. A. Omirov +1
The present paper is devoted to the investigation of properties of Cartan subalgebras and regular elements in Leibniz -algebras. The relationship between Cartan subalgebras and…
n-Dimensional filiform Leibniz algebras of length (n-1) and their derivations
S. Albeverio, Sh. A. Ayupov, B. A. Omirov +1
In this work -dimensional filiform Leibniz algebras admitting a gradation of length are classified. Derivations of such algebras are also described.