Derived Hall algebras of root categories
报告题目: Derived Hall algebras of root categories
For a finitary hereditary abelian category A, we define a derived Hall algebra
of its root category by counting the triangles and using the octahedral axiom, which is
proved to be isomorphic to the Drinfeld double of Hall algebra of A. When applied to
finite-dimensional nilpotent representations of the Jordan quiver or coherent sheaves over
elliptic curves, these algebras provide categorical realizations of the Drinfeld double of the
ring of symmetric functions and also double affine Hecke algebras.