For an associative algebra A, the famous theorem of Loday, Quillen and Tsygan says that there is an isomorphism between the graded symmetric product of the cyclic homology of A and the Lie algebra homology of the infinite matrices gl (A), as commutative and cocommutative Hopf algebras. This paper aims to study a deformation and quantization of this isomorphism. We show that if A is a Koszul Calabi-Yau algebra, then the primitive part of the Lie algebra homology H_ (gl (A) ) has a Lie bialgebra structure which is induced from the Poincar\'e duality of A and deforms H_ (gl (A) ) to a co-Poisson bialgebra. Moreover, there is a Hopf algebra which quantizes such a co-Poisson bialgebra, and the Loday-Quillen-Tsygan isomorphism lifts to the quantum level, which can be interpreted as a quantization of the tangent map from the tangent complex of BGL to the tangent complex of K-theory.
Chen et al. (Wed,) studied this question.