Differential graded Brauer groups

2023/08/17 by Zimmermann, Alexander
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2308.08980

Abstract

We consider central simple K-algebras which happen to bedifferential graded K-algebras. Two such algebras A and Bare considered equivalent if there are bounded complexes of finite dimensionalK-vector spaces C_A and C_B such that the differential graded algebras A⊗_K \rm End_K^\bullet(C_A) and B⊗_K \rm End_K^\bullet(C_B) are isomorphic.Equivalence classes form an abelian group, which we call thedg Brauer group.We prove that this group is isomorphic to the ordinary Brauer group of the field K.

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