math.QA — Quantum Algebra

Unipotent tensor categories and pronilpotent Lie quasibialgebras

Contributed by Pavel I Etingof

We construct a bijection between tensor equivalence classes of unipotent tensor categories over $\C$ and continuous Lie quasibialgebras with linearly compact pronilpotent underlying Lie algebra, modulo continuous isomorphisms and classical twists. The bijection is defined using a fixed universal quantization functor and solves the problem raised in Remark~4.6 of arXiv:0708.1487 by Etingof and Gelaki. The proof combines reconstruction with filtered dequantization modulo twists and convergence of universal formulas. A category admits a tensor fiber functor precisely when a classical twist removes its curvature.