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Hall algebras and the Quantum Frobenius

Kevin McGerty
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Abstract

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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Kevin McGerty. 2009-11-23. Hall algebras and the Quantum Frobenius. https://doi.org/10.1215/00127094-2010-036

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