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math.QA2002
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…
math.QA2002
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…
math.QA2002
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…