Equivariant Zariski Structures

Details Equivariant Zariski Structures Equivariant Zariski Structures

2011-10-22

arxiv.org/abs/1110.4964v1

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A category of equivariant algebras is defined, after introducing some important examples (the first Weyl algebra, $U_{q}(sl_{2}(k))$ for generic q, 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 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.

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