2023/07/17 by Érica Z. Fornaroli, Mykola Khrypchenko, Fornaroli, Érica Z. +1
Mathematics · #16S50 #55U10 #55U15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary: 16W25 #Rings and Algebras (math.RA) #secondary: 06A11
paper · pdf · doi:10.48550/arxiv.2307.08439
openalex publication_date 2023/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of the paper we describe φ-derivations of the incidence algebra I(X,K) of a locally finite poset X over a field K, where φ is an arbitrary automorphism of I(X,K). We show that they admit decompositions similar to that of usual derivations of I(X,K). In particular, the quotient of the space of φ-derivations of I(X,K) by the subspace of inner φ-derivations of I(X,K) is isomorphic to the first group of certain cohomology of X, which is developed in the second part of the paper.