25 citations · 94 across the 25 of their papers we have counts for
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Quantum affine algebras at small root of unity
Simon D. Lentner
We study the Frobenius-Lusztig kernel for quantum affine algebras at root of unity of small orders that are usually excluded in literature. These cases are somewhat degenerate and…
A theorem on roots of unity and a combinatorial principle
Simon Lentner, Daniel Nett
Given a finite set of roots of unity, we show that all power sums are non-negative integers iff the set forms a group under multiplication. The main argument is purely combinatoria…
New -matrices for small quantum groups
Simon Lentner, Daniel Nett
In this article we construct a large family of -matrices for various extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices b…
A Frobenius homomorphism for Lusztig's quantum groups over arbitrary roots of unity
Simon D. Lentner
For a finite dimensional semisimple Lie algebra and a root of unity, Lusztig defined an infinite dimensional quantum group of divided powers. Under certain restrictions on the orde…
Factorization of Graded Traces on Nichols Algebras
Simon Lentner, Andreas Lochmann
We study the factorization of the Hilbert series and more general graded traces of a Nichols algebra into cyclotomic polynomials. Nichols algebras play the role of Borel subalgebra…
Partially dualized Hopf algebras have equivalent Yetter-Drinfel'd modules
Alexander Barvels, Simon Lentner, Christoph Schweigert
Given a Hopf algebra and a projection to a Hopf subalgebra, we construct a Hopf algebra , called the partial dualization of , with a projection to the Hopf al…