16 citations · 24 across the 7 of their papers we have counts for
7 papers
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…
Divisibility Relations for the Dimensions and Hilbert series of Nichols Algebras of Non-Abelian Group Type
Andreas Lochmann
We present a divisibility relation for the dimensions and Hilbert series of certain classes of Nichols algebras of non-abelian group type, which generalizes Nichols algebras over C…
Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
I. Heckenberger, A. Lochmann, L. Vendramin
We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichol…
Shared Rough and Quasi-Isometries of Groups
Andreas Lochmann
We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi…
Irreducible Elements in Metric Lattices
Andreas Lochmann
We describe a natural generalization of irreducibility in order lattices with arbitrary metrics. We analyse the special cases of valuation metrics and more general metrics for latt…
Rough Isometries of Lipschitz Function Spaces
Andreas Lochmann
We show that rough isometries between metric spaces X, Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their…
An Analysis of the Transition Zone Between the Various Scaling Regimes in the Small-World Model
Andreas Lochmann, Manfred Requardt
We analyse the so-called small-world network model (originally devised by Strogatz and Watts), treating it, among other things, as a case study of non-linear coupled difference or…