arXiv subjects

F. N. Arzikulov

Publications and source records attributed to F. N. Arzikulov.

5 recordsLinked to original sources

arXiv2026

2-Local and local derivations on Jordan matrix rings over commutative involutive rings

In the present paper we prove that every 2-local inner derivation on the Jordan ring of self-adjoint matrices over a commutative involutive ring is a derivation. We also apply our technique to various Jordan algebras of infinite dimensional self-adjoint matrix-valued maps on a set and prove that every 2-local spatial derivation on such algebras is a spatial derivation. It is also proved that every local spatial derivation on the same Jordan algebras is a derivation.

math.RA↗

arXiv2023

Local and 2-local derivations of the octonion algebra

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.

math.RA↗

arXiv2023

Local and 2-local automorphisms of finite-dimensional nilpotent associative algebras

In the present paper automorphisms, local and 2-local automorphisms of $n$-dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these algebras is clarified. It turns out that the common form of the matrix of an automorphism on these algebras does not coincide with the local automorphism's matrices common form on these algebras. Therefore, these associative algebras have local automorphisms that are not automorphisms. Also, that each 2-local automorphism of these algebras is an automorphism is proved.

math.RA↗

arXiv2021

Local and 2-local automorphisms of some solvable Leibniz algebras

In this paper we prove that any local automorphism on the solvable Leibniz algebras with null-filiform and naturally graded non-Lie filiform nilradicals, whose dimension of complementary space is maximal is an automorphism. Furthermore, the same problem concerning 2-local automorphisms of such algebras is investigated and we obtain the analogously results for 2-local automorphisms.

math.RA↗

arXiv2013

Infinite order decompositions of C$^*$-algebras

In the given article infinite order decompositions of C$^*$-algebras are investigated. We give complete proofs of the following statements: 1) If the order unit space $\sum_{ξ,η}^\oplus p_ξAp_η$ is monotone complete in $B(H)$ (i.e. ultraweakly closed), then $\sum_{ξ,η}^\oplus p_ξAp_η$ is a C$^*$-algebra. 2) If $A$ is monotone complete in $B(H)$ (i.e. a von Neumann algebra), then $A=\sum_{ξ,η}^\oplus p_ξAp_η$. 3) If $\sum_{ξ,η}^\oplus p_ξAp_η$ is a C$^*$-algebra then this algebra is a von Neumann algebra.

math.OA↗