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Transposed Poisson structures on Lie incidence algebras | | Ivan Kaygorodov
; Mykola Khrypchenko
; | | Date: |
1 Sep 2023 | | Abstract: | Let $X$ be a finite connected poset, $K$ a field of characteristic zero and
$I(X,K)$ the incidence algebra of $X$ over $K$ seen as a Lie algebra under the
commutator product. In the first part of the paper we show that any
$frac{1}{2}$-derivation of $I(X,K)$ decomposes into the sum of a
central-valued $frac 12$-derivation, an inner $frac{1}{2}$-derivation and a
$frac{1}{2}$-derivation associated with a map $sigma:X^2_< o K$ that is
constant on chains and cycles in $X$. In the second part of the paper we use
this result to prove that any transposed Poisson structure on $I(X,K)$ is the
sum of a structure of Poisson type, a mutational structure and a structure
determined by $lambda:X^2_e o K$, where $X^2_e$ is the set of $(x,y)in X^2$
such that $x<y$ is a maximal chain not contained in a cycle. | | Source: | arXiv, 2309.00332 | | Services: | Forum | Review | PDF | Favorites | |
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