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 the Koszul dual coalgebra.
Bocklandt, Graded Calabi Yau algebras of dimension 3,J
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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 the Koszul dual coalgebra.