# Shifted quiver quantum toroidal algebra and subcrystal representations

@article{Noshita2022ShiftedQQ,
title={Shifted quiver quantum toroidal algebra and subcrystal representations},
author={Go Noshita and Akimi Watanabe},
journal={Journal of High Energy Physics},
year={2022}
}
• Published 5 September 2021
• Mathematics
• Journal of High Energy Physics
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 particular, shifted QY acts on general subcrystals of the original BPS crystal. A trigonometric deformation called quiver quantum toroidal algebra (QQTA) was also proposed and shown to act on the same BPS crystal. Unlike QY, QQTA has a formal Hopf superalgebra structure which is useful in deriving…
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