Geodesic
PBW THEOREMS AND FROBENIUS STRUCTURES FOR QUANTUM MATRICES
Glasgow mathematical journal, Tome 49 (2007) no. 3, pp. 479-488

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DOI

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].
DOI : 10.1017/S0017089507003813
Mots-clés : Primary 20G42, Secondary 81R50 
GAVARINI, FABIO. PBW THEOREMS AND FROBENIUS STRUCTURES FOR QUANTUM MATRICES. Glasgow mathematical journal, Tome 49 (2007) no. 3, pp. 479-488. doi: 10.1017/S0017089507003813
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     title = {PBW {THEOREMS} {AND} {FROBENIUS} {STRUCTURES} {FOR} {QUANTUM} {MATRICES}},
     journal = {Glasgow mathematical journal},
     pages = {479--488},
     year = {2007},
     volume = {49},
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     doi = {10.1017/S0017089507003813},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003813/}
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