Automorphisms of the total digraph for the ring of square matrices over a field

C. Costara; A. E. Guterman; A. M. Maksaev; V. V. Promyslov

doi:10.1016/j.laa.2023.03.007

Automorphisms of the total digraph for the ring of square matrices over a field

C. Costara, A. E. Guterman, A. M. Maksaev, V. V. Promyslov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we characterize the automorphisms of the total graph for the ring M_n of matrices of order n≥2 over any field with at least 3 elements. To do this, we apply the technique of maps preserving matrix invariants; in particular, as an intermediate step, we characterize pairs of surjective maps φ₁,φ₂:M_n→M_n such that A+B is singular if and only if φ₁(A)+φ₂(B) is singular.

Original language	English
Pages (from-to)	129-143
Number of pages	15
Journal	Linear Algebra and Its Applications
Volume	666
DOIs	https://doi.org/10.1016/j.laa.2023.03.007
State	Published - 1 Jun 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.

Funding

The work of A.M. Maksaev was supported by the HSE University Basic Research Program. The work of V.V. Promyslov was supported by the Russian Science Foundation under the grant no. 22-11-00052 .

Funders	Funder number
Russian Science Foundation	22-11-00052
National Research University Higher School of Economics

Keywords

Automorphisms of graphs
Determinant
Nonlinear preserver

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10.1016/j.laa.2023.03.007

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Automorphisms of the total digraph for the ring of square matrices over a field

Abstract

Bibliographical note

Funding

Keywords

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