Pre-Calabi-Yau structures and moduli of representations

Wai-Kit Yeung

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arXiv · 1802.05398

Pre-Calabi-Yau structures and moduli of representations

Wai-Kit Yeung

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Abstract

We establish a system of formal noncommutative calculus for differential forms and polyvector fields, which forms the foundations for the study of pre-Calabi-Yau categories. Using an explicit trace map, we show that any $n$-Calabi-Yau structure on a non-positively graded dg algebra $A$ induces a $(2-n)$-shifted symplectic structure on its derived moduli stack of representations; while any $n$-pre-Calabi-Yau structure on $A$ induces a $(2-n)$-shifted Poisson structure on this derived moduli stack.

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BibTeX RIS

Wai-Kit Yeung. 2022-02-19. Pre-Calabi-Yau structures and moduli of representations. https://arxiv.org/abs/1802.05398

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