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Transposed Poisson structures on generalized Witt algebras and Block Lie algebras  Ivan Kaygorodov
; Mykola Khrypchenko
;  Date: 
1 Feb 2023  Abstract:  We describe transposed Poisson structures on generalized Witt algebras
$W(A,V, langle cdot,cdot
angle )$ and Block Lie algebras $L(A,g,f)$ over a
field $F$ of characteristic zero, where $langle cdot,cdot
angle$ and $f$
are nondegenerate. More specifically, if $dim(V)>1$, then all the transposed
Poisson algebra structures on $W(A,V,langle cdot,cdot
angle)$ are trivial;
and if $dim(V)=1$, then such structures are, up to isomorphism, mutations of
the group algebra structure on $FA$. The transposed Poisson algebra structures
on $L(A,g,f)$ are in a onetoone correspondence with commutative and
associative multiplications defined on a complement of the square of $L(A,g,f)$
with values in the center of $L(A,g,f)$. In particular, all of them are usual
Poisson structures on $L(A,g,f)$. This generalizes earlier results about
transposed Poisson structures on Block Lie algebras $mathcal{B}(q)$.  Source:  arXiv, 2302.00403  Services:  Forum  Review  PDF  Favorites 


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