Non-trivial stably free modules over crossed products
نویسندگان
چکیده
منابع مشابه
Non-trivial stably free modules over crossed products
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 befo...
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Let R be a commutative ring. When an R-module has a particular module-theoretic property after direct summing it with a finite free module, it is said to have the property stably. For example, R-modules M and N are stably isomorphic if Rk ⊕M ∼= Rk ⊕N for some k ≥ 0. An R-module M is stably free if it is stably isomorphic to a free module: Rk ⊕M is free for some k. When M is finitely generated a...
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We prove that for any finite-dimensional ringR and n ≥ dimR+2, the group En(R[X]) acts transitively on Umn(R[X]). In particular, we obtain that for any finite-dimensional ringR, all finitely generated stably free modules over R[X] of rank > dimR are free. This result was only known for Noetherian rings. The proof we give is short, simple, and constructive.
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In the first part of this paper we introduce a simplified version of a new Black Box from Shelah [11] which can be used to construct complicated אn-free abelian groups for any natural number n ∈ N. In the second part we apply this prediction principle to derive for many commutative rings R the existence of אn-free R-modules M with trivial dual M ∗ = 0, where M∗ = Hom(M, R). The minimal size of ...
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Given a quasi-special endomorphism ρ of a C∗ -algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by ρ . Exploiting some aspects of the underlying generalized Doplicher-Roberts duality theory based on Pimsner algebras, an obstruction to the existence of such extensions is found and described in terms of sections of a suitable ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2009
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/42/33/335209