Derived Hall algebras

DOI10.1215/S0012-7094-06-13536-6zbMath1117.18011arXivmath/0501343MaRDI QIDQ860115

Bertrand Toën

Publication date: 23 January 2007

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0501343

zbMATH Keywords

Hall algebradifferential graded categoryAbelian categoryHall number

Mathematics Subject Classification ID

Related Items (66)

A parameterization of the canonical bases of affine modified quantized enveloping algebras ⋮ Generalized Kac–Moody Lie Algebras and Product Quivers ⋮ Quillen-Segal algebras and Stable homotopy theory ⋮ Bridgeland's Hall algebras of tilted algebras and Lusztig's symmetries ⋮ Derived Hall Algebras and Lattice Algebras ⋮ On derived Hall numbers for tame quivers ⋮ Decomposition spaces, incidence algebras and Möbius inversion. I: Basic theory ⋮ Higher Categorical Aspects of Hall Algebras ⋮ Towers and fibered products of model structures ⋮ Bridgeland’s Hall algebras and Heisenberg doubles ⋮ A note on Bridgeland Hall algebras ⋮ 2-Segal spaces as invertible infinity-operads ⋮ Hall algebras associated to complexes of fixed size ⋮ Hall algebras of extriangulated categories ⋮ \(\imath\)Quantum groups of split type via derived Hall algebras ⋮ Stability conditions and derived Hall algebras ⋮ Hall algebras and quantum symmetric pairs I: Foundations ⋮ THE HALL ALGEBRAS OF SURFACES I ⋮ Bifibrations and weak factorisation systems ⋮ Derived Hall algebras of one-cycle gentle algebras: the infinite global dimension case ⋮ Gröbner-Shirshov basis of derived Hall algebra of type \(A_n\) ⋮ On the Hall algebra of an elliptic curve. I. ⋮ Quantum groups via Hall algebras of complexes. ⋮ Acyclic quantum cluster algebras via Hall algebras of morphisms ⋮ On two Hall algebra approaches to odd periodic triangulated categories ⋮ Some remarks on triangulated categories and Kac-Moody algebras ⋮ Hall algebras of odd periodic triangulated categories. ⋮ Adelic models of tensor-triangulated categories ⋮ Bridgeland stability, 2-Segal spaces, and the Ran space of the line ⋮ Unnamed Item ⋮ Some remarks on Bridgeland’s Hall algebras ⋮ Hall algebras associated to triangulated categories ⋮ Toën's formula and Green's formula ⋮ Modified Ringel-Hall algebras, Green's formula and derived Hall algebras ⋮ Functorial factorizations in the category of model categories ⋮ Configurations in abelian categories. IV: Invariants and changing stability conditions ⋮ Legendrian skein algebras and Hall algebras ⋮ Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds ⋮ The Hall algebra of a curve ⋮ Flags and tangles ⋮ Homotopy fiber products of homotopy theories ⋮ From triangulated categories to cluster algebras ⋮ Proofs of the integral identity conjecture over algebraically closed fields ⋮ Double Hall algebras and derived equivalences. ⋮ Moduli of objects in dg-categories ⋮ Semi-derived Ringel-Hall algebras and Drinfeld double ⋮ On the cluster multiplication theorem for acyclic cluster algebras ⋮ Complete Segal spaces arising from simplicial categories ⋮ AR quivers, exceptional sequences and algorithms in derived Hall algebras ⋮ A short proof of Green's formula ⋮ A realization of quantum groups via product valued quivers ⋮ Cyclic complexes, Hall polynomials and simple Lie algebras. ⋮ Topological K-theory of complex noncommutative spaces ⋮ Lie algebras arising from 1-cyclic perfect complexes ⋮ Modified Ringel-Hall algebras, naive lattice algebras and lattice algebras ⋮ Descente fidèlement plate pour les n-champs d’Artin ⋮ Multiplicative properties of certain elements in Bridgeland Hall algebras ⋮ Braid group symmetries on quasi-split \(\imath\)quantum groups via \(\imath\)Hall algebras ⋮ A proof of the $\ell$-adic version of the integral identity conjecture for polynomials ⋮ Quantum cluster characters of Hall algebras revisited ⋮ A study of symmetric functions via derived Hall algebra ⋮ Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras ⋮ The Bridgeland's Ringel-Hall algebra associated to an algebra with global dimension at most two. ⋮ Remarks on Hall algebras of triangulated categories ⋮ The Grothendieck construction for model categories ⋮ On the composition subalgebras of Bridgeland’s Hall algebras

Cites Work

• Unnamed Item
• The homotopy theory of dg-categories and derived Morita theory
• Homotopy commutative diagrams and their realizations
• Hall algebras and quantum groups
• Heisenberg doubles and derived categories
• A Quillen model structure on the category of dg categories
• Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
• Homotopical algebraic geometry. II. Geometric stacks and applications
• The minimal resolution of the ideal of a general arrangement of a big number of points in \(\mathbb{P}^ n\)

This page was built for publication: Derived Hall algebras