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Pre-Calabi-Yau structures and moduli of representations
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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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Cited by 1 Pith paper
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Deformation and quantization of the Loday-Quillen-Tsygan isomorphism for Calabi-Yau categories
For Koszul Calabi-Yau algebras, the Loday-Quillen-Tsygan isomorphism deforms to a co-Poisson bialgebra isomorphism and quantizes to a Hopf algebra isomorphism, induced from the Lie bialgebra on the cyclic homology of ...
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