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PreprintCC BY 4.0arXiv

Quantization of Preprojective Algebras and the Type A Rational Cherednik Algebra

  • Meiliang Liu
  • Jun Zhang
  • Hu Zhao
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Abstract

For the Jordan quiver, we construct a radial quantum trace morphism from the quantum preprojective algebra to the algebra of invariant differential operators on the Cartan subalgebra. Its classical limit recovers the classical trace morphism associated with the commuting quotient, and we prove that both the quantum and classical trace morphisms are surjective. We further relate noncommutative quantizations of the Jordan preprojective algebra to the spherical rational Cherednik algebra of type A. Finally, we derive explicit formulas for the Harish--Chandra homomorphism and its radial part in power-sum coordinates.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026quantization,
  title = {{Quantization of Preprojective Algebras and the Type A Rational Cherednik Algebra}},
  author = {Meiliang Liu and Jun Zhang and Hu Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15206},
  eprint = {2609.15206},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15206},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Quantization of Preprojective Algebras and the Type A Rational Cherednik Algebra
AU  - Meiliang Liu
AU  - Jun Zhang
AU  - Hu Zhao
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15206
UR  - https://arxiv.org/abs/2609.15206
AB  - For the Jordan quiver, we construct a radial quantum trace morphism from the quantum preprojective algebra to the algebra of invariant differential operators on the Cartan subalgebra. Its classical limit recovers the classical trace morphism associated with the commuting quotient, and we prove that both the quantum and classical trace morphisms are surjective. We further relate noncommutative quantizations of the Jordan preprojective algebra to the spherical rational Cherednik algebra of type A. Finally, we derive explicit formulas for the Harish--Chandra homomorphism and its radial part in power-sum coordinates.
ER  -