Submission date: 22 October 2011

Abstract:

A category of equivariant algebras is defined after introducing some important examples (e.g. first Weyl algebra, certain quantum tori at generic parameter). To each equivariant algebra, a first-order theory is assigned. Model-theoretic results are established (uncountable categoricity, quantifier elimination to the level of positive existential formulas) and that an appropriate dimension theory exists for models, making them Zariski structures. A functor from the category of equivariant algebras to the category of Zariski structures is defined and further properties of equivariant structures are briefly discussed.

Mathematics Subject Classification: 03C65

Keywords and phrases: Zariski structures, noncommutative algebraic geometry, geometric representation theory, quantized algebras.

Full text arXiv 1110.4964: pdf, ps.