10 citations · 16 across the 8 of their papers we have counts for
9 papers
A novel Non-Homogeneous Local Representation of the Braid Group
Arash Pourkia
We construct a non-homogeneous local representation of the braid group by tracking the labels of individual strands through successive crossings. Each generator acts through…
A basic dimensional representation of Artin braid group , and a general Burau representation
Arash Pourkia
Burau representation of the Artin braid group remains as one of the very important representations for the braid group. Partly, because of its connections to the Alexander polynomi…
Solutions to the constant Yang-Baxter equation in all dimensions
Arash Pourkia
We will present solutions to the constant Yang-Baxter equation, in any dimension . More precisely, for any , we will create an infinite family of by matrices whic…
A note on "eight-vertex" universal quantum gates
Arash Pourkia
Many well-known and well-studied four by four universal quantum logic gates in the literature are of a specific form, the so called eight-vertex form \eqref{8vertexform} \cite{kauf…
Cyclic groups and quantum logic gates
Arash Pourkia, J. Batle, C. H. Raymond Ooi
We present a formula for an infinite number of universal quantum logic gates, which are by unitary solutions to the Yang-Baxter (Y-B) equation. We obtain this family from a…
Enveloping algebras of some quantum Lie algebras
Arash Pourkia
We define a family of Hopf algebra objects, , in the braided category of -modules (known as anyonic vector spaces), for which the property $ψ^2_{H\otimes H}=id_{H\…
A note on Hopf Cyclic Cohomology in Non-symmetric Monoidal Categories
Arash Pourkia
In our previous work, Hopf cyclic cohomology in braided monoidal categories, we extended the formalism of Hopf cyclic cohomology due to Connes and Moscovici and the more general ca…
A Super Version of the Connes-Moscovici Hopf Algebra
Masoud Khalkhali, Arash Pourkia
We define a super version of the Connes-Moscovici Hopf algebra, . For that, we consider the supergroup of orientation preserving diffe…
Hopf cyclic cohomology in braided monoidal categories
Masoud Khalkhali, Arash Pourkia
We extend the formalism of Hopf cyclic cohomology to the context of braided categories. For a Hopf algebra in a braided monoidal abelian category we introduce the notion of stable…