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 language | English |
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Article number | 335209 |
Pages (from-to) | 1-11 |
Number of pages | 11 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 42 |
Issue number | 33 |
DOIs | |
Publication status | Published - 2009 |
ASJC Scopus subject areas
- Mathematical Physics
- Modelling and Simulation
- Statistics and Probability
- General Physics and Astronomy
- Statistical and Nonlinear Physics