In September 2000, at the Centre de Recerca Matematica in Barcelona, we pre sented a 30-
hour Advanced Course on Algebraic Quantum Groups. After the course, we expanded and …

Given any (commutative) field k and any iterated Ore extension R= k [X1][X2; σ2, δ2]⋯[XN;
σN, δN] satisfying some suitable assumptions, we construct the so-called “Derivative …

We study prime and primitive ideals in a unified setting applicable to quantizations (at
nonroots of unity) of $ n\times n $ matrices, of Weyl algebras, and of Euclidean and …

Brown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any
complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson …

This paper offers an expository account of some ideas, methods, and conjectures
concerning quantized coordinate rings and their semiclassical limits, with a particular focus …

SYMPLECTIC LEAVES OF COMPLEX REDUCTIVE POISSON-LIE GROUPS Page 1 DUKE
MATHEMATICAL JOURNAL Vol. 112, No. 3, c 2002 SYMPLECTIC LEAVES OF COMPLEX …

The structure of Poisson polynomial algebras of the type obtained as semiclassical limits of
quantized coordinate rings is investigated. Sufficient conditions for a rational Poisson action …

Abstract We prove the Berenstein–Zelevinsky conjecture that the quantized coordinate rings
of the double Bruhat cells of all finite-dimensional connected, simply connected simple …

Abstract We prove the Andruskiewitsch–Dumas conjecture that the automorphism group of
the positive part of the quantized universal enveloping algebra U _q (g) U q (g) of an …

Abstract Joseph and Hodges–Levasseur (in the A case) described the spectra of all
quantum function algebras $ R_q [G] $ on simple algebraic groups in terms of the centers of …