Differential graded Brauer groups
Alexander Zimmermann (UPJV, LAMFA)

TL;DR
This paper introduces the dg Brauer group, an extension of the classical Brauer group to differential graded algebras, and proves their isomorphism over a field.
Contribution
It defines the dg Brauer group for differential graded algebras and establishes its isomorphism with the classical Brauer group of the field.
Findings
The dg Brauer group is isomorphic to the classical Brauer group.
Differential graded algebras can be classified via this new group.
The result bridges differential graded algebra theory with classical algebraic structures.
Abstract
We consider central simple -algebras which happen to bedifferential graded -algebras. Two such algebras and are considered equivalent if there are bounded complexes of finite dimensional-vector spaces and such that the differential graded algebras and 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 .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
