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- W4225996914 abstract "Given a Lie groupoid $mathcal{G}$ over $M$, $A$ the tangent Lie algebroid of $mathcal{G}$, and $rho: Arightarrow TM$ the anchor map, we provide a formula that decomposes an arbitrary multiplicative $k$-form $Theta$ on $mathcal{G}$ into two parts. The first part is $e$, a $1$-cocycle of $mathfrak{J}mathcal{G}$ valued in $wedge^k T^*M$, and the second part is $thetain Gamma(A^*otimes (wedge^{k-1} T^*M))$ which is $rho$-compatible, meaning that $iota_{rho(u)}theta(u)=0$ for all $uin A$. We call this pair of data $(e,theta)$ the $(0,k)$-characteristic pair of $Theta$. Next, we prove that if $mathcal{G}$ is a Poisson Lie groupoid, then the space $Omega^{bullet}_{mathrm{mult}}(mathcal{G})$ of multiplicative forms on $mathcal{G}$ has a differential graded Lie algebra (DGLA) structure. Furthermore, when combined with $Omega^bullet(M)$, which is the space of forms on the base manifold $M$, $Omega^{bullet}_{mathrm{mult}}(mathcal{G})$ forms a canonical DGLA crossed module. This supplements a previously known fact that multiplicative multivector fields on $mathcal{G}$ form a DGLA crossed module with the Schouten algebra $Gamma(wedge^bullet A)$ stemming from the tangent Lie algebroid $A$." @default.
- W4225996914 created "2022-05-05" @default.
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- W4225996914 date "2022-01-17" @default.
- W4225996914 modified "2023-09-26" @default.
- W4225996914 title "Multiplicative forms on Poisson groupoids" @default.
- W4225996914 doi "https://doi.org/10.48550/arxiv.2201.06242" @default.
- W4225996914 hasPublicationYear "2022" @default.
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