Zariski topologies on stratified spectra of quantum algebras

A framework is developed to describe the Zariski topologies on the prime and primitive spectra of a quantum algebra A in terms of the (known) topologies on strata of these spaces and maps between the collections of closed sets of different strata. A conjecture is formulated, under which the desired maps would arise from homomorphisms between certain central subalgebras of localized factor algebras of A. When the conjecture holds, spec A and prim A are then determined, as topological spaces, by a finite collection of (classical) affine algebraic varieties and morphisms between them. The conjecture is verified for Oq(GL2(k)), Oq(SL3(k)), and Oq(M2(k)) when q is a non-root of unity and the base field k is algebraically closed

Zariski topologies on stratified spectra of quantum algebras

A framework is developed to describe the Zariski topologies on the prime and primitive spectra of a quantum algebra A in terms of the (known) topologies on strata of these spaces and maps between the collections of closed sets of different strata. A conjecture is formulated, under which the desired maps would arise from homomorphisms between certain central subalgebras of localized factor algebras of A. When the conjecture holds, spec A and prim A are then determined, as topological spaces, by a finite collection of (classical) affine algebraic varieties and morphisms between them. The conjecture is verified for Oq(GL2(k)), Oq(SL3(k)), and Oq(M2(k)) when q is a non-root of unity and the base field k is algebraically closed