Geodesic
On automorphisms and derivations of reduced incidence algebras and coalgebras
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 90 (2024), pp. 33-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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Incidence algebras of partially ordered sets over commutative rings are an important and characteristic example of function rings. From a partially ordered set, one can obtain an incidence coalgebra. Using certain equivalence relations on the set of all intervals of a locally finite poset, reduced incidence algebras and reduced incidence coalgebras are defined. These objects have a much more complex structure compared to incidence algebras and incidence coalgebras. This article introduces two types of automorphisms of the reduced incidence algebra -multiplicative and order, as well as one type of derivations - additive derivation. As for incidence coalgebras, there are no works devoted to their automorphisms or derivations. The article discusses a possible approach to the study of automorphisms and derivations of incidence coalgebras.
Keywords: incidence algebra, derivation.
Mots-clés : incidence coalgebra, automorphism 
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P. A. Krylov; T. D. Norbosambuev. On automorphisms and derivations of reduced incidence algebras and coalgebras. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 90 (2024), pp. 33-39. http://geodesic.mathdoc.fr/item/VTGU_2024_90_a2/

[1] Spiegel E., O'Donnell C.J., Incidence Algebras, Marcel Dekker, New York, 1997 | MR | Zbl

[2] Krylov P., Tuganbaev A., Incidence rings: automorphisms and derivations, 2023, arXiv: 2305.02984 [math.RA] | MR