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.
Loday--Quillen--Tsygan Theorem for Coalgebras
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In this paper we prove that Loday--Quillen--Tsygan Theorem generalizes to the case of coalgebras. Specifically, we show that the Chevalley--Eilenberg--Lie homology of the Lie coalgebra of infinite matrices over a coassociative coalgebra $C$ is generated by the cyclic homology of the underlying coalgebra $C$ as an exterior algebra.
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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.