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Quantum unique factorisation domains
S Launois, T H Lenagan, L Rigal
We prove a general theorem showing that iterated skew polynomial extensions of the type which fit the conditions needed by Cauchon's deleting derivations theory and by the Goodearl…
Quantum graded algebras with a straightening law and the AS-Cohen-Macaulay property for quantum determinantal rings and quantum grassmannians
T H Lenagan, L Rigal
We study quantum analogues of quotient varieties, namely quantum grassmannians and quantum determinantal rings, from the point of view of regularity conditions. More precisely, we…
The maximal order property for quantum determinantal rings
T H Lenagan, L Rigal
We develop a method of reducing the size of quantum minors in the algebra of n x n quantum matrices. The method is used to show that quantum determinantal factor rings of n x n qua…
Ring theoretic properties of quantum grassmannians
A C Kelly, T H Lenagan, L Rigal
The m x n quantum grassmannian, G_q(m,n), is the subalgebra of the algebra of m x n quantum matrices that is generated by the maximal m x m quantum minors. Several properties of G_…
The first fundamental theorem of coinvariant theory for the quantum general linear group
K. R. Goodearl, T. H. Lenagan, L. Rigal
We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum general and special linear groups on tensor products of quantum matrix algebras.…