Non-trivial stably free modules over crossed products

Details Non-trivial stably free modules over crossed products Non-trivial stably free modules over crossed products

2009-03-23

arxiv.org/abs/0903.3766v1

Journal of Physics A, 42 (2009) 335209

Mathematics

Rings and Algebras

13 pages

Scientific paper

10.1088/1751-8113/42/33/335209

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.

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