Trace decategorification of categorified quantum sl2

in Mathematische Annalen (2017), 367(1), 397440

The trace or the 0th Hochschild–Mitchell homology of a linear category C may be regarded as a kind of decategorification of C. We compute the traces of the two versions U˙ and U∗ of categorified quantum ... [more ▼]

The trace or the 0th Hochschild–Mitchell homology of a linear category C may be regarded as a kind of decategorification of C. We compute the traces of the two versions U˙ and U∗ of categorified quantum sl2 introduced by the third author. The trace of U is isomorphic to the split Grothendieck group K_0(U˙), and the higher Hochschild–Mitchell homology of U˙ is zero. The trace of U∗ is isomorphic to the idempotented integral form of the current algebra U(sl2[t]). [less ▲]