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Derived Hall algebras for stable homotopy theories. (English) Zbl 1277.55010

Hall algebras, defined initially for abelian categories, play an important role in representation theory. Toën constructed derived Hall algebras associated to triangulated categories arising as homotopy categories of model categories whose objects are modules over a sufficiently finitary differential graded category over \(\mathbb{F}_q\). In this paper, the author modifies Toën’s proofs to establish derived Hall algebras corresponding to triangulated categories arising as homotopy categories for more general stable homotopy theories, in particular stable complete Segal spaces satisfying appropriate finiteness assumptions.

MSC:

55U35 Abstract and axiomatic homotopy theory in algebraic topology
55U40 Topological categories, foundations of homotopy theory
18G55 Nonabelian homotopical algebra (MSC2010)
18E30 Derived categories, triangulated categories (MSC2010)
16S99 Associative rings and algebras arising under various constructions
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