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Piotr Krylov

Publications and source records attributed to Piotr Krylov.

6 recordsLinked to original sources
arXiv2024

Multiplicative Automorphisms of Incidence Algebras

Let $I(X,R)$ be the incidence algebra of the preordered set $X$ over the ring $R$. In the case of a finite connected partially ordered set $X$, we prove that the subgroup of inner multiplicative automorphisms is a direct factor of the group of multiplicative automorphisms of the algebra $I(X,R)$. As a consequence, we obtain several matching criteria of the subgroup of inner multiplicative automorphisms with the group of multiplicative automorphisms.

math.RA↗
arXiv2023

Incidence Coalgebras: Automorphisms and Derivations

We describe automorphisms and derivations of the incidence coalgebra $\text{Co}(X,F)$ of the partially ordered set $X$ over a field $F$. In this case, the fact is significantly used that the dual algebra of the coalgebra $\text{Co}(X,F)$ is isomorphic to the incidence algebra $I(X,F)$ of the partially ordered set $X$ over the field $F$.

math.RA↗
arXiv2023

Formal Matrix Rings: Isomorphism Problem

We consider the isomorphism problem for formal matrix rings over a given ring. Principal factor matrices of such rings play an important role in this case. The work is supported by Russian Scientific Foundation, project 23-21-00375 (P.A. Krylov) and project 22-11-00052 (A.A. Tuganbaev).

math.RA↗
arXiv2022

On Realization and Isomorphism Problems for Formal Matrix Rings

We consider realization and isomorphism problems for formal matrix rings over a given ring. Principal multiplier matrices of such rings play an important role in this case.\\ The work of A.A.Tuganbaev is supported by Russian Scientific Foundation, project 22-11-00052.

math.RA↗
arXiv2022

Automorphisms of Formal Matrix Rings

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

math.RA↗