On Some Linear Mappings of Incidence Coalgebras

Authors

DOI:

https://doi.org/10.52575/2687-0959-2024-56-4-273-285

Keywords:

Automorphism, Derivation, Incidence Algebra, Incidence Coalgebra

Abstract

Various linear mappings of the incidence algebra I(X, F) of the partially ordered set X over a field F have always attracted attention of specialists. Automorphisms, isomorphisms, derivations, antiautomorphisms and involutions have been studied. Works that would study linear mappings of the incidence coalgebra Co(X, F) are unknown. This coalgebra is in some sense a dual object to the algebra I(X, F). This paper reveals the structure of the automorphism group and the derivation space of the coalgebra Co(X, F). It is found that the group of automorphisms of the coalgebra Co(X, F) is antiisomorphic to the group of automorphisms of the algebra I(X, F), while the derivation spaces of these objects are isomorphic. The proofs are based on the well-known fact that the dual algebra to the coalgebra Co(X, F) is canonically isomorphic to the algebra I(X, F).


Acknowledgements
The research of the second and third authors has been conducted at the expense of the Russian Science Foundation.

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Author Biographies

Evgeniy V. Kaigorodov, Gorno-Altaisk State University

Candidate of Physical and Mathematical Sciences, Assosiate Professor of the Department of Mathematics, Physics and Computer Science, Gorno-Altaisk State University,
Gorno-Altaisk, Russia
E-mail: gazetaintegral@gmail.com
ORCID: 0000-0001-5172-5915

Piotr A. Krylov, National Research Tomsk State University

Doctor of Physical and Mathematical Sciences, Professor f the Department of Algebra, National Research Tomsk State University,
Tomsk, Russia
E-mail: krylov@math.tsu.ru
ORCID: 0000-0002-9631-0075

Askar A. Tuganbaev, National Research University "Moscow Power Engineering Institute"

Doctor of Physical and Mathematical Sciences, Professor of the Department of Higher Mathematics, National Research University "Moscow Power Engineering Institute",
Moscow, Russia
E-mail: tuganbaev@gmail.com
ORCID: 0000-0001-9582-3314

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Published

2024-12-30

How to Cite

Kaigorodov, E. V., Krylov, P. A., & Tuganbaev, A. A. (2024). On Some Linear Mappings of Incidence Coalgebras. Applied Mathematics & Physics, 56(4), 273-285. https://doi.org/10.52575/2687-0959-2024-56-4-273-285

Issue

Vol. 56 No. 4 (2024)

Section

Mathematics

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