538 citations
- Royal ObservatoryGB6 papers
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6 papers · 1 filter
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…
Representation rings of quantum groups
M. Domokos, T. H. Lenagan
Generators and relations are given for the subalgebra of cocommutative elements in the quantized coordinate rings of the classical groups, where the deformation parameter q is tran…
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_…
Weakly multiplicative coactions of quantized function algebras
M Domokos, T H Lenagan
A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra…