Commutators in the Endomorphism Ring of a Complex
  According to an old result of Albert and Muckenhoupt, the commutators in the endomorphism ring of a finite dimensional vector space are precisely the elements of trace zero. We replace the finite dimensional vector space with a complex of finite dimensional vector spaces, and characterize commutators and other elements with commutator-like properties in terms of appropriately defined traces. 
Steven E. Landsburg
math.AC math.RA