Stephane Launois

QUANTUM UNIQUE FACTORISATION DOMAINS

We prove a general theorem showing that iterated skew polynomial extensions of the type that fit the conditions needed by Cauchons deleting derivations theory and by the Goodearl-Letzter stratification theory are unique factorisation rings in the sense of Chatters and Jordan. This general result applies to many quantum algebras; in particular, generic quantum matrices and quantized enveloping algebras of the nilpotent part of a semisimple Lie algebra are unique factorisation domains in the sense of Chatters. The result also extends to generic quantum grassmannians (by using noncommutative dehomogenisation) and to the quantum groups Oq (GLn) and Oq (SLn).

Quantum Cluster Algebra Structures on Quantum Grassmannians and their Quantum Schubert Cells: The Finite-type Cases

We exhibit quantum cluster algebra structures on quantum GrassmanniansKq[Gr(2;n)] and their quantum Schubert cells, as well as onKq[Gr(3; 6)],Kq[Gr(3; 7)] andKq[Gr(3; 8)]. These cases are precisely those where the quantum cluster algebra is of nite type and the structures we describe quantize those found by Scott for the classical situation.

Primitive ideals in quantum Schubert cells: Dimension of the strata

Abstract. The aim of this paper is to study the representation theory of quantum Schubert cells. Let 𝔤

RANK t ℋ-PRIMES IN QUANTUM MATRICES

\mathfrak {g}

Graded quantum cluster algebras and an application to quantum Grassmannians

be a simple complex Lie algebra. To each element w of the Weyl group W of 𝔤

Efficient Recognition of Totally Nonnegative Matrix Cells

\mathfrak {g}

From totally nonnegative matrices to quantum matrices and back, via Poisson geometry

, De Concini, Kac and Procesi have attached a subalgebra U q [w]

Twisted Poincaré Duality for some Quadratic Poisson Algebras

U_q[w]

Poisson algebras via model theory and differential algebraic geometry

of the quantised enveloping algebra U q (𝔤)

Endomorphisms of Quantum Generalized Weyl Algebras

U_q(\mathfrak {g})