Related papers: Reduced quiver quantum toroidal algebras
We establish a connection between a generalization of KLR algebras, called quiver Schur algebras, and the cohomological Hall algebras of Kontsevich and Soibelman. More specifically, we realize quiver Schur algebras as algebras of…
We define a quantum loop group $\mathbf{U}^+_Q$ associated to an arbitrary quiver $Q=(I,E)$ and maximal set of deformation parameters, with generators indexed by $I \times \mathbb{Z}$ and some explicit quadratic and cubic relations. We…
We present results, both old and new, concerning Koszul and G-quadratic properties of algebras associated with points, curves, cubics and spaces of quadrics of low codimension.
Given a quiver $Q$, a formal potential is called analytic if its coefficients are bounded by the terms of a geometric series. As shown by Toda, the potentials appearing in the deformation theory of complexes of coherent sheaves on complex…
We consider the motivic Hall algebra of coherent sheaves over an irreducible reduced projective curve of arithmetic genus $1$. We introduce the composition subalgebra in the singular curve case, and show that it is isomorphic to the…
Quantum toroidal algebras (or double affine quantum algebras) are defined from quantum affine Kac-Moody algebras by using the Drinfeld quantum affinization process. They are quantum groups analogs of elliptic Cherednik algebras (elliptic…
In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the…
We study the quiver with relations of the endomorphism algebra of an APR tilting module. We give an explicit description of the quiver with relations by graded quivers with potential (QPs) and mutations. The result also implies that…
We develop the connection between the preprojective $K$-theoretic Hall algebra of a quiver $Q$ and the quantum loop group associated to $Q$ via stable envelopes of Nakajima quiver varieties.
We use derived Hall algebra of the category of nilpotent representations of Jordan quiver to reconstruct the theory of symmetric functions, focusing on Hall-Littlewood symmetric functions and various operators acting on them.
In this letter, we use quantum quasi-shuffle algebras to construct Rota-Baxter algebras, as well as tridendriform algebras. We also propose the notion of braided Rota-Baxter algebras, which is the relevant object of Rota-Baxter algebras in…
We establish an embedding of the quantum enveloping algebra of a symmetric generalized Kac--Moody algebra into a localized Hall algebra of $\mathbb Z_2$-graded complexes of representations of a quiver with (possible) loops. To overcome…
We present a new family of quantum Weyl algebras where the polynomial part is the quantum analog of functions on homogeneous spaces corresponding to symmetric matrices, skew symmetric matrices, and the entire space of matrices of a given…
We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are…
The statistical model of crystal melting represents BPS configurations of D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the quiver Yangian, acts consistently on the…
In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody…
We give a short introduction to Cohomological Hall algebras of quivers and describe the semistable Cohomological Hall algebra of central slope of the Kronecker quiver in terms of generators and relations.
We find a quantum group structure in two-dimensional motion of nonrelativistic electrons in a uniform magnetic field on a torus. The representation basis of the quantum algebra is composed of the quantum Hall wavefunctions proposed by…
We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$, and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of…
In this paper, the singular Ringel-Hall algebra for a tame quiver is introduced and shown to be isomorphic to the positive part of the quantum extended Kac-Moody algebra. A PBW basis is constructed and a new class of perverse sheaves is…