Non-trivial stably free modules over crossed products

Natalia Iyudu, R.A. Wisbauer

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.
Original languageEnglish
Article number335209
Pages (from-to)1-11
Number of pages11
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number33
DOIs
Publication statusPublished - 2009

ASJC Scopus subject areas

  • Mathematical Physics
  • Modelling and Simulation
  • Statistics and Probability
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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