Skew derivations of incidence algebras
In the first part of the paper we describe $\varphi$-derivations of the incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$, where $\varphi$ 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 par...
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| creator | Fornaroli, Érica Z Khrypchenko, Mykola |
| description | In the first part of the paper we describe $\varphi$-derivations of the
incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$,
where $\varphi$ 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 $\varphi$-derivations of $I(X,K)$ by
the subspace of inner $\varphi$-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. |
| doi_str_mv | 10.48550/arxiv.2307.08439 |
| format | Article |
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incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$,
where $\varphi$ 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 $\varphi$-derivations of $I(X,K)$ by
the subspace of inner $\varphi$-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.</description><identifier>DOI: 10.48550/arxiv.2307.08439</identifier><language>eng</language><subject>Mathematics - Rings and Algebras</subject><creationdate>2023-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2307.08439$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2307.08439$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Fornaroli, Érica Z</creatorcontrib><creatorcontrib>Khrypchenko, Mykola</creatorcontrib><title>Skew derivations of incidence algebras</title><description>In the first part of the paper we describe $\varphi$-derivations of the
incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$,
where $\varphi$ 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 $\varphi$-derivations of $I(X,K)$ by
the subspace of inner $\varphi$-derivations of $I(X,K)$ is isomorphic to the
first group of certain cohomology of $X$, which is developed in the second part
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incidence algebra $I(X,K)$ of a locally finite poset $X$ over a field $K$,
where $\varphi$ 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 $\varphi$-derivations of $I(X,K)$ by
the subspace of inner $\varphi$-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.</abstract><doi>10.48550/arxiv.2307.08439</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Rings and Algebras |
| title | Skew derivations of incidence algebras |
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