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arXiv · 2103.09491

Shifted symplectic and Poisson structures on global quotients

Wai-Kit Yeung
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Abstract

For a derived stack obtained as a quotient of a derived affine scheme by a reductive group, we show that shifted symplectic structures can be characterized by the Cartan-de Rham complex. For non-reductive groups, we also show the analogous statement for Getzler's extension of the Cartan-de Rham complex. Dually, we construct a Cartan model for polyvector fields on global quotients by reductive groups, and show that shifted Poisson structures can be characterized by it.

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Wai-Kit Yeung. 2021-03-17. Shifted symplectic and Poisson structures on global quotients. https://arxiv.org/abs/2103.09491

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