The nonstandard quantum plane

Annals of Pure and Applied Logic 156 (1):78-85 (2008)
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Abstract

Let Uq be the quantum group associated to sl2 with char≠2 and qk not a root of unity. The article is devoted to the model-theoretic study of the quantum plane kq[x,y], considered as an -structure, where is the language of representations of Uq. It is proved that the lattice of definable k-subspaces of kq[x,y] is complemented. This is deduced from the same result for the Uq-module M, which is defined to be the direct sum of all finite dimensional representations of Uq. It follows that the ring of definable scalars for the quantum plane is a von Neumann regular epimorphic ring extension of the quantum group Uq

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Model Theory and Modules.Mike Prest - 1989 - Journal of Symbolic Logic 54 (3):1115-1118.

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