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This is a Quantitative Study study.

October 9, 2025Open Access

Deformation and quantization of the Loday-Quillen-Tsygan isomorphism for Calabi-Yau categories

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This research demonstrates a deformation of cyclic homology in Koszul Calabi-Yau algebras, suggesting new structures in Lie algebra homology.

The study reveals that the primitive part of Lie algebra homology exhibits a Lie bialgebra structure, enhancing our understanding of Calabi-Yau algebras.
The deformation to a co-Poisson bialgebra indicates a deep connection between homological algebra and quantum structures in this context.
A constructed Hopf algebra successfully quantizes the co-Poisson bialgebra, offering new insights into the quantum realm of algebraic structures.
The Loday-Quillen-Tsygan isomorphism's lift to the quantum level highlights its significance in bridging classical and quantum algebraic concepts.

Chen et al. (2025) studied this question.

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This research demonstrates a deformation of cyclic homology in Koszul Calabi-Yau algebras, suggesting new structures in Lie algebra homology.