Sep 19, 2024
Dr. Christine Uhl, associate professor of Mathematics, recently had two peer-reviewed articles published.
Her work “Automorphisms of quantum polynomial rings and Drinfeld Hecke algebras,” coauthored with Anne Shepler (University of North Texas), appeared in the Journal of Noncommutative Geometry in April.
This work extends some of the results from her dissertation and uses a combinatorial approach, which allows some results of Hochschild cohomology over fields of characteristic zero to be extended to fields of arbitrary characteristic.
Her paper “Schur-Weyl duality for toroidal algebras of type A” (with coauthors Chari, Grimley, Lin, Mangum, and Wilson) appeared in Communications in Algebra in June. This work was partially funded by a Structured Quartet Research Ensemble (SQuaRE) at the American Institute of Mathematics. This paper proves an analog of the Schur-Weyl duality for a quotient of the classical 2-toroidal Lie algebra of type A.