# A note on quiver quantum toroidal algebra

@article{Noshita2022ANO,
title={A note on quiver quantum toroidal algebra},
author={Go Noshita and Akimi Watanabe},
journal={Journal of High Energy Physics},
year={2022}
}
• Published 16 August 2021
• Mathematics
• Journal of High Energy Physics
Abstract Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian $$\mathfrak{gl}$$ gl 1. The characteristic feature of the algebra is the action on BPS states for non-compact toric Calabi-Yau threefolds, which are in one-to-one correspondence with the crystal melting models. These algebras can be bootstrapped from the action on the crystals and have various truncations.In this paper, we propose a q-deformed…
2 Citations
Toroidal and elliptic quiver BPS algebras and beyond
• Mathematics
Journal of High Energy Physics
• 2022
Abstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce
Quiver Yangians and Crystal Melting: A Concise Summary
The goal of this short article is to summarize some of the recent developments in the quiver Yangians and crystal meltings. This article is based on a lecture delivered by the author at International

## References

SHOWING 1-10 OF 71 REFERENCES
Toroidal and elliptic quiver BPS algebras and beyond
• Mathematics
Journal of High Energy Physics
• 2022
Abstract The quiver Yangian, an infinite-dimensional algebra introduced recently in [1], is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce
q-deformation of corner vertex operator algebras by Miura transformation
• Mathematics
• 2021
Recently, Gaiotto and Rapcak proposed a generalization of WN algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as
Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
The quantum toroidal algebra of $gl_1$ provides many deformed W-algebras associated with (super) Lie algebras of type A. The recent work by Gaiotto and Rapcak suggests that a wider class of deformed
Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Mathematics
• 2017
A bstractReflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal gl1$$\mathfrak{g}{\mathfrak{l}}_1$$). Webs of DIM
Webs of W-algebras
• Mathematics
Journal of High Energy Physics
• 2018
A bstractWe associate vertex operator algebras to (p, q)-webs of interfaces in the topologically twisted N=4$$\mathcal{N}=4$$ super Yang-Mills theory. Y-algebras associated to trivalent junctions
Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds.
• Mathematics
• 2020
To a smooth local toric Calabi-Yau 3-fold $X$ we associate the Heisenberg double of the (equivariant spherical) Cohomological Hall algebra in the sense of Kontsevich and Soibelman. This Heisenberg
Quantum algebraic approach to refined topological vertex
• Mathematics
• 2011
A bstractWe establish the equivalence between the refined topological vertex of Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of type W1+∞ introduced by Miki. Our
Quiver Yangian from crystal melting
• Mathematics
Journal of High Energy Physics
• 2020
Abstract We find a new infinite class of infinite-dimensional algebras acting on BPS states for non-compact toric Calabi-Yau threefolds. In Type IIA superstring compactification on a toric
Quiver W-algebras
• Mathematics
• 2015
For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the