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Enveloping algebras with just infinite Gelfand–Kirillov dimension

Natalia K. Iyudu School of Mathematics, University of Edinburgh, United Kingdom Susan J. Sierra School of Mathematics, University of Edinburgh, United Kingdom

Rings and Algebras mathscidoc:2203.31003

Arkiv for Matematik, 58, (2), 285-306, 2020.11
Let g be the Witt algebra or the positive Witt algebra. It is well known that the enveloping algebra U(g) has intermediate growth and thus infinite Gelfand–Kirillov (GK-) dimension. We prove that the GK-dimension of U(g) is just infinite in the sense that any proper quotient of U(g) has polynomial growth. This proves a conjecture of Petukhov and the second named author for the positive Witt algebra. We also establish the corresponding results for quotients of the symmetric algebra S(g) by proper Poisson ideals. In fact, we prove more generally that any central quotient of the universal enveloping algebra of the Virasoro algebra has just infinite GK-dimension. We give several applications. In particular, we easily compute the annihilators of Verma modules over the Virasoro algebra.
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@inproceedings{natalia2020enveloping,
  title={Enveloping algebras with just infinite Gelfand–Kirillov dimension},
  author={Natalia K. Iyudu, and Susan J. Sierra},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311095628334603944},
  booktitle={Arkiv for Matematik},
  volume={58},
  number={2},
  pages={285-306},
  year={2020},
}
Natalia K. Iyudu, and Susan J. Sierra. Enveloping algebras with just infinite Gelfand–Kirillov dimension. 2020. Vol. 58. In Arkiv for Matematik. pp.285-306. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220311095628334603944.
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