# 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…

## 2 Citations

Toroidal and elliptic quiver BPS algebras and beyond

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- 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

- 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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Toroidal and elliptic quiver BPS algebras and beyond

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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
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