# 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} }

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…

## 5 Citations

### Toroidal and elliptic quiver BPS algebras and beyond

- MathematicsJournal 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 $\mathcal{W}$-Algebras for Generalized Conifolds

- Mathematics
- 2022

We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach in literature. We also prove that the quiver Yangians related…

### 5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$

- Mathematics
- 2022

We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition…

### Quantum loop groups for arbitrary quivers

- Mathematics
- 2022

. We study the dual constructions of quantum loop groups and Feigin-Odesskii type shuﬄe algebras for an arbitrary quiver, for which the ar- row parameters are arbitrary non-zero elements of any ﬁeld.…

### Quiver Yangians and Crystal Melting: A Concise Summary

- Mathematics
- 2022

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…

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- MathematicsJournal of High Energy Physics
- 2022

Abstract
Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In…

### Toroidal and elliptic quiver BPS algebras and beyond

- MathematicsJournal 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…

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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…