%0 Journal Article
%T Quantum Grothendieck rings and derived Hall algebras
%A David Hernandez
%A Bernard Leclerc
%J Mathematics
%D 2011
%I arXiv
%X We obtain a presentation of the t-deformed Grothendieck ring of a quantum loop algebra of Dynkin type A, D, E. Specializing t at the the square root of the cardinality of a finite field F, we obtain an isomorphism with the derived Hall algebra of the derived category of a quiver Q of the same Dynkin type. Along the way, we study for each choice of orientation Q a tensor subcategory whose t-deformed Grothendieck ring is isomorphic to the positive part of a quantum enveloping algebra of the same Dynkin type, where the classes of simple objects correspond to Lusztig's dual canonical basis.
%U http://arxiv.org/abs/1109.0862v3