8 problems

A quantized coordinate ring is a noncommutative algebra serving as a quantum analogue of the coordinate ring of an affine algebraic variety, and its prime spectrum consists of its…

Let $V$ be a variety with commutative coordinate ring $\mathcal{O}(V)$, and let $\mathcal{O}_q(V)$ be a more general quantization of it. Goodearl's conjecture. The space…

Let $R$ be a ${\mathbb K}$-algebra with a rational action of the ${\mathbb K}$-torus $H$ by algebra automorphisms satisfying condition (C). Let $I\subset J$ be $H$-primes in $R$. C…

Brown–Goodearl conjecture.

Goodearl's quantum–Poisson correspondence conjecture. The algebra $A$ should belong to a flat family of $k$-algebras with semiclassical limit $\mathcal{O}(V)$, and there should be…

Kaplansky's conjecture. These two properties characterize the prime spectrum of a commutative ring.

Assume that the base field $\mathbb{K}$ has characteristic zero and that $q\in\mathbb{K}^{\ast}$ is not a root of unity. Let the algebra of quantum matrices be the corresponding qu…

Let $V$ be an affine algebraic variety over an algebraically closed field $\mathbb{K}$ of characteristic zero. Let a generic quantised coordinate ring of $V$ have semiclassical lim…