Enveloping algebras with just infinite Gelfand-Kirillov dimension

Natalia K. Iyudu, Susan J. Sierra

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.
Original languageEnglish
Pages (from-to)285-306
JournalArkiv for Matematik
Volume58
Issue number2
DOIs
Publication statusPublished - 31 Oct 2020

Keywords / Materials (for Non-textual outputs)

  • math.RA
  • math-ph
  • math.AG
  • math.MP
  • math.QA
  • math.RT
  • 16S30, 17B68, 16P90, 17B65

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