Abstract
We construct a Hennings-type logarithmic invariant for restricted quantum at a root of unity. This quantum group is not quasitriangular and hence not ribbon, but factorizable. The invariant is defined for a pair: a –manifold and a colored link inside . The link is split into two parts colored by central elements and by trace classes, or elements in the Hochschild homology of , respectively. The two main ingredients of our construction are the universal invariant of a string link with values in tensor powers of , and the modified trace introduced by the third author with his collaborators and computed on tensor powers of the regular representation. Our invariant is a colored extension of the logarithmic invariant constructed by Jun Murakami.
Citation
Anna Beliakova. Christian Blanchet. Nathan Geer. "Logarithmic Hennings invariants for restricted quantum ${\mathfrak{sl}}(2)$." Algebr. Geom. Topol. 18 (7) 4329 - 4358, 2018. https://doi.org/10.2140/agt.2018.18.4329
Information