[en] 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]).
Disciplines :
Mathématiques
Auteur, co-auteur :
Beliakova, Anna; Universität Zürich - UZH > Institute of Mathematics
Habiro, Kazuo; Kyoto University > Research Institute for Mathematical Sciences
Lauda, Aaron D.; University of Southern California > Department of Mathematics
ZIVKOVIC, Marko ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Trace decategorification of categorified quantum sl2
