Duke Mathematical Journal

Hall algebras and quantum Frobenius

Kevin Mcgerty

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Abstract

Lusztig constructed a Frobenius morphism for quantum groups at an 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

Article information

Source
Duke Math. J., Volume 154, Number 1 (2010), 181-206.

Dates
First available in Project Euclid: 14 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1279140508

Digital Object Identifier
doi:10.1215/00127094-2010-036

Mathematical Reviews number (MathSciNet)
MR2668556

Zentralblatt MATH identifier
1237.17019

Subjects
Primary: 17B35: Universal enveloping (super)algebras [See also 16S30]
Secondary: 16A64

Citation

Mcgerty, Kevin. Hall algebras and quantum Frobenius. Duke Math. J. 154 (2010), no. 1, 181--206. doi:10.1215/00127094-2010-036. https://projecteuclid.org/euclid.dmj/1279140508


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