We show that arising out of noncommutative geometry is a natural family of edge Laplacians
on the edges of a graph. The family includes a canonical edge Laplacian associated to the …

We show how to do gauge theory on the octonions and other nonassociative algebras such
as “quasi-R 4” models proposed in string theory. We use the theory of quasialgebras …

We study super-braided Hopf algebras Λ primitively generated by finite-dimensional right
crossed (or Drinfeld-Radford-Yetter) modules Λ 1 over a Hopf algebra A which are quotients …

We study noncommutative differential structures on the group of permutations SN, defined
by conjugacy classes. The 2-cycles class defines an exterior algebra ΛN which is a super …

We systematically extend the elementary differential and Riemannian geometry of classical
U (1)-gauge theory to the noncommutative setting by combining recent advances in …

We study the noncommutative Riemannian geometry of the alternating group A 4=(Z 2× Z
2)⋊ Z 3 using the recent formulation for finite groups. We find a unique 'Levi …

We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf
algebras. One of our examples is the Fomin–Kirillov algebra E 3 E_3. Another one appeared …

We compute the noncommutative de Rham cohomology for the finite dimensional q-
deformed coordinate ring C q SL 2 at odd roots of unity and with its standard four …

This is a self-contained introduction to quantum Riemannian geometry based on quantum
groups as frame groups, and its proposed role in quantum gravity. Much of the article is …

Over fields of characteristic zero, we determine all absolutely irreducible Yetter–Drinfeld
modules over groups that have prime dimension and yield a finite-dimensional Nichols …