23 citations · 107 across the 43 of their papers we have counts for
28 papers · 1 filter
Derivations and Hochschild cohomology of quantum nilpotent algebras
Stéphane Launois, Samuel A. Lopes, Isaac Oppong
We compute the derivations of Quantum Nilpotent Algebras under a technical (but necessary) assumption on the center. As a consequence, we give an explicit description of the first…
Is of type
Stéphane Launois, Isaac Oppong
By a theorem of Dixmier, primitive quotients of enveloping algebras of finite-dimensional complex nilpotent Lie algebras are isomorphic to Weyl algebras. In view of this result, it…
Derivations and the first Hochschild cohomology group of the quantum grassmannian
Stéphane Launois, Tom Lenagan
We calculate the derivations and the first Hochschild cohomology group of the quantum grassmannian over a field of characteristic zero in the generic case when the deformation para…
The automorphism group of the quantum grassmannian
Stéphane Launois, Tom Lenagan
We calculate the automorphism group of the generic quantum grassmannian.
Quantum Grassmannians and their Associated Quantum Schubert Varieties at roots of unity
Jason P. Bell, Stéphane Launois, Alexandra Rogers
We study the PI degree of various quantum algebras at roots of unity, including quantum Grassmannians, quantum Schubert varieties, partition subalgebras, and their associated quant…
Derivations of a family of quantum second Weyl algebras
S Launois, I Oppong
In view of a well-known theorem of Dixmier, its is natural to consider primitive quotients of as quantum analogues of Weyl algebras. In this work, we study th…
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…
Total positivity is a quantum phenomenon: the grassmannian case
Stéphane Launois, Tom Lenagan, Brendan Nolan
The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the quantum grassmannian. More precisely, under the assumption that the defo…
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…
On the automorphisms of quantum Weyl algebras
A. P. Kitchin, S. Launois
Motivated by Weyl algebra analogues of the Jacobian conjecture and the Tame Generators problem, we prove quantum versions of these problems for a family of analogues to the Weyl al…
A strong Dixmier-Moeglin equivalence for quantum Schubert cells
Jason Bell, Stéphane Launois, Brendan Nolan
Dixmier and Moeglin gave an algebraic condition and a topological condition for recognising the primitive ideals among the prime ideals of the universal enveloping algebra of a fin…
Poisson algebras via model theory and differential-algebraic geometry
Jason Bell, Stéphane Launois, Omar León Sánchez +1
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 p…
Endomorphisms of quantum generalized Weyl algebras
A. P. Kitchin, S. Launois
We prove that every endomorphism of a simple quantum generalized Weyl algebra over a commutative Laurent polynomial ring in one variable is an automorphism. This is achieved by…
A quadratic Poisson Gel'fand-Kirillov problem in prime characteristic
Stephane Launois, Cesar Lecoutre
The quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is Poisson birationally equivalent to a Poisson affine space, i.e. to a pol…
Graded quantum cluster algebras and an application to quantum Grassmannians
Jan E. Grabowski, Stéphane Launois
We introduce a framework for -gradings on cluster algebras (and their quantum analogues) that are compatible with mutation. To do this, one chooses the degrees of the (…
Automorphisms of quantum matrices
S. Launois, T. H. Lenagan
We study the automorphism group of the algebra $\oqmn$ of generic quantum matrices. We provide evidence for our conjecture that this group is generated by the transpos…
Enumeration of torus-invariant strata with respect to dimension in the big cell of the quantum minuscule Grassmannian of type B_n
Jason Bell, Karel Casteels, Stéphane Launois
The aim of this article is to give explicit formulae for various generating functions, including the generating function of torus-invariant primitive ideals in the big cell of the…
Enumeration of $\C{H}$-strata in quantum matrices with respect to dimension
Jason Bell, Karel Casteels, Stéphane Launois
We present a combinatorial method to determine the dimension of $\C{H}$-strata in the algebra of quantum matrices $\Oq$ as follows. To a given $\C{H}$-stratum we associ…
Primitive ideals in quantum Schubert cells: dimension of the strata
Jason Bell, Karel Casteels, Stéphane Launois
The aim of this paper is to study the representation theory of quantum Schubert cells. Let $\g$ be a simple complex Lie algebra. To each element of the Weyl group of $\g$,…
Quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells: the finite-type cases
Jan E. Grabowski, Stéphane Launois
We exhibit quantum cluster algebra structures on quantum Grassmannians and their quantum Schubert cells, as well as on , and $K_q[Gr(3,8…
From totally nonnegative matrices to quantum matrices and back, via Poisson geometry
S. Launois, T. H. Lenagan
In this survey article, we describe recent work that connects three separate objects of interest: totally nonnegative matrices; quantum matrices; and matrix Poisson varieties.
Twisting the quantum grassmannian
S Launois, T H Lenagan
In contrast to the classical and semiclassical settings, the Coxeter element (12...n) which cycles the columns of an mxn matrix does not determine an automorphism of the quantum gr…
Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves
K. R. Goodearl, S. Launois, T. H. Lenagan
The algebra of quantum matrices of a given size supports a rational torus action by automorphisms. It follows from work of Letzter and the first named author that to understand the…
Prime ideals in the quantum grassmannian
S Launois, T H Lenagan, L Rigal
We consider quantum Schubert cells in the quantum grassmannian and give a cell decomposition of the prime spectrum via the Schubert cells. As a consequence, we show that all primes…