Commutators in the Endomorphism Ring of a Complex

2016/08/04 by Landsburg, Steven E.
#Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1608.01425

Abstract

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.

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