Abstract
A new class of noncommutative k-algebras (for k an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first-order theory is assigned describing models of a suitable corresponding geometric space. Model-theoretic results for these geometric structures are established (uncountable categoricity, quantifier elimination to the level of existential formulas) and that an appropriate dimension theory exists, making them Zariski structures.
| Original language | English |
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| Pages (from-to) | 786-804 |
| Number of pages | 18 |
| Journal | Journal of the London Mathematical Society |
| Volume | 91 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 19 May 2015 |