Investigators have not been able to determine the cause of a fire at an Amherst apartment complex last year that killed a University of Massachusetts student. The blaze on Jan. 21, 2013, took the life of James Hoffman, 21, a business major from Stoughton. An autopsy determined that he died of smoke inhalation. The State Fire Marshal’s office said the fire at Rolling Green apartments started directly in front of the closet in Hoffman’s second-floor bedroom, but investigators were not able to identify any known heat source. More than 30 people were displaced by the fire.