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Derivations of the idealization of the incidence module over the finitary incidence algebra
Abstract
Let R be a unital commutative ring and X a partially ordered set. Let FI(X,R) and I(X,R) be the finitary incidence algebra and the incidence module of X over R, respectively, and let D(X,R)=FI(X,R)⊕ I(X,R) be the idealization of the FI(X,R)-bimodule I(X,R). We give a description of the Lie algebra of derivations of D(X,R) and also provide some necessary or sufficient conditions on R and X for the description of this Lie algebra to be simpler.
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BibTeX
@misc{fornaroli2026derivations,
title = {{Derivations of the idealization of the incidence module over the finitary incidence algebra}},
author = {Érica Zancanella Fornaroli and Roger Emanuel Moraes Pezzott},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24120},
eprint = {2610.24120},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24120},
}
RIS
TY - UNPB
TI - Derivations of the idealization of the incidence module over the finitary incidence algebra
AU - Érica Zancanella Fornaroli
AU - Roger Emanuel Moraes Pezzott
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24120
UR - https://arxiv.org/abs/2610.24120
AB - Let R be a unital commutative ring and X a partially ordered set. Let FI(X,R) and I(X,R) be the finitary incidence algebra and the incidence module of X over R, respectively, and let D(X,R)=FI(X,R)⊕ I(X,R) be the idealization of the FI(X,R)-bimodule I(X,R). We give a description of the Lie algebra of derivations of D(X,R) and also provide some necessary or sufficient conditions on R and X for the description of this Lie algebra to be simpler.
ER -