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PBW THEOREMS AND FROBENIUS STRUCTURES FOR QUANTUM MATRICES
FABIO GAVARINI
Journal:

Glasgow Mathematical Journal / Volume 49 / Issue 3 / September 2007

Published online by Cambridge University Press:

01 September 2007, pp. 479-488

Print publication:

September 2007
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Let , let be the quantum function algebra – over – associated to G, and let be the specialisation of the latter at a root of unity ϵ, whose order ℓ is odd. There is a quantum Frobenius morphism that embeds the function algebra of G, in as a central Hopf subalgebra, so that is a module over . When , it is known by [3], [4] that (the complexification of) such a module is free, with rank ℓdim(G). In this note we prove a PBW-like theorem for , and we show that – when G is Matn or GLn – it yields explicit bases of over . As a direct application, we prove that and are free Frobenius extensions over and , thus extending some results of [5].