58 citations · 319 across the 55 of their papers we have counts for
25 papers · 1 filter
Binomial ideals in quantum tori and quantum affine spaces
K. R. Goodearl
The article targets binomial ideals in quantum tori and quantum affine spaces. First, noncommutative analogs of known results for commutative (Laurent) polynomial rings are obtaine…
Spectra of quantum algebras
K. R. Goodearl
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structu…
Catenarity in quantum nilpotent algebras
K. R. Goodearl, S. Launois
In this paper, it is established that quantum nilpotent algebras (also known as CGL extensions) are catenary, i.e., all saturated chains of inclusions of prime ideals between any t…
Integral quantum cluster structures
K. R. Goodearl, M. T. Yakimov
We prove a general theorem for constructing integral quantum cluster algebras over , namely that under mild conditions the integral forms of quantum nilp…
Tauvel's height formula for quantum nilpotent algebras
K R Goodearl, S Launois, T H Lenagan
Tauvel's height formula, which provides a link between the height of a prime ideal and the Gelfand-Kirillov dimension of the corresponding factor algebra, is verified for quantum n…
The Berenstein-Zelevinsky quantum cluster algebra conjecture
K. R. Goodearl, M. T. Yakimov
We prove the Berenstein-Zelevinsky conjecture that the quantized coordinate rings of the double Bruhat cells of all finite dimensional simple algebraic groups admit quantum cluster…