Hall algebras and the Quantum Frobenius

Details Hall algebras and the Quantum Frobenius Hall algebras and the Quantum Frobenius

2006-01-09

arxiv.org/abs/math/0601150v4

Mathematics

Quantum Algebra

Final version: typos corrected and exposition improved

Scientific paper

Lusztig has constructed a Frobenius morphism for quantum groups at an
$\ell$-th root of unity, which gives an integral lift of the Frobenius map on
universal enveloping algebras in positive characteristic. Using the Hall
algebra we give a simple construction of this map for the positive part of the
quantum group attached to an arbitrary Cartan datum in the nondivisible case.

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