On the $K$-theoretic Hall algebra of a surface

Abstract

In this paper, we define the $K$-theoretic Hall algebra for $0$-dimensional coherent sheaves on a smooth projective surface, prove that the algebra is associative and construct a homomorphism to a redefined shuffle algebra analogous to Negut.

References in corpus (8)

• The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of ${\mathbb{A}}^2$
• Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra
• Two-dimensional categorified Hall algebras
• Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
• K-theory and cohomology of algebraic stacks: Riemann-Roch theorems, D-modules and GAGA theorems
• Operational K-theory
• On the irreducibility of the punctual Quotient Scheme of a Surface
• Virtual pullbacks in $K$-theory

Cited by in corpus (9)

• Quiver Yangian from Crystal Melting
• Two-dimensional categorified Hall algebras
• A slow review of the AGT correspondence
• Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces
• A Categorical Quantum Toroidal Action on Hilbert Schemes
• Generators for categorical Hall algebras of surfaces
• The Wheel Conditions and K-theoretic Hall Algebras
• Hall-type algebras for categorical Donaldson-Thomas theories on local surfaces
• A Serre Relation in the $K$-theoretic Hall algebra of surfaces