9 citations · 9 across the 3 of their papers we have counts for
7 papers
Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
J. Scott Carter, Mohamed Elhamdadi, Matias Graña +1
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the cas…
Knot theory for self-indexed graphs
Matias Graña, Vladimir Turaev
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally aris…
Quantization of non-unitary geometric classical r-matrices
P. Etingof, M. Graña
In this paper we explicitly attach to a geometric classical r-matrix (not necessarily unitary), a geometric (i.e., set-theoretical) quantum R-matrix , which is a quantizatio…
Indecomposable racks of order p^2
Matias Graña
We classify indecomposable racks of order p^2 (p a prime). There are 2p^2 - 2p - 2 isomorphism classes, among which 2p^2 - 3p - 1 correspond to quandles. In particular, we prove th…
On rack cohomology
Pavel Etingof, Matias Grana
We prove that the lower bounds for Betti numbers of the rack, quandle and degeneracy cohomology given by Carter, Jelsovsky, Kamada, and Saito, are in fact equalities. We compute as…
Pointed Hopf algebras of dimension 32
Matias Graña
We give a complete classification of the 32-dimensional pointed Hopf algebras over an algebraically closed field k with characteristic different from 2. It turns out that there are…