Higher Dimensional Multiparameter Unitary and Nonunitary Braid Matrices: Even Dimensions (2007)
Abdesselam, B., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
A class of $(2n)^2\times(2n)^2$ multiparameter braid matrices are presented for all $n$ $(n\geq 1)$. Apart from the spectral parameter $\theta$, they depend on $2n^2$ free parameters...
Abdesselam, B., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We construct $(2n)^2\times (2n)^2$ unitary braid matrices $\hat{R}$ for $n\geq 2$ generalizing the class known for $n=1$. A set of $(2n)\times (2n)$ matrices $(I,J,K,L)$ are defined. $\hat{R}$ is...
q-Plane Wave Solutions of q-Weyl gravity (2007)
We give solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves.
On a "New" Deformation of GL(2) (2007)
Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We refute a recent claim in the literature of a "new" quantum deformation of GL(2).
Exotic Bialgebra S03: Representations, Baxterisation and Applications (2006)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of...
Duality and Representations for New Exotic Bialgebras (2005)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Duality for Exotic Bialgebras (2005)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2005)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
Exotic bialgebras : non-deformation quantum groups (2004)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of solutions of the Yang--Baxter equation, there are solutions that are not deformations of the trivial solution (essentially the identity). We consider the algebras defined by...
Duality and Representations for New Exotic Bialgebras (2003)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Duality and Representations for New Exotic Bialgebras (2003)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We study the geometric aspects of two exotic bialgebras S03 and S14 introduced in math.QA/0206053. These bialgebras are obtained by the Faddeev-Reshetikhin-Takhtajan RTT prescription with...
Duality and Representations for New Exotic Bialgebras (2002)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We find the exotic matrix bialgebras which correspond to the two non-triangular nonsingular 4x4 R-matrices in the classification of Hietarinta, namely, R_{S0,3} and R_{S1,4}. We find two new exotic...
Duality for Exotic Bialgebras (2001)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
Duality for Exotic Bialgebras (2001)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
Duality for Exotic Bialgebras (2001)
Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
In the classification of Hietarinta, three triangular $4\\times 4$ $R$-matrices lead, via the FRT formalism, to matrix bialgebras which are not deformations of the trivial one. In this paper, we find...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2000)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2000)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
On Combined Standard-Nonstandard or Hybrid (q,h)-Deformations (2000)
Aneva, B. L., Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
Combined $(q,h)$-deformations proposed by Kupershmidt and Ballesteros-Herranz-Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard $q$-deformation. We...
Duality for the Jordanian Matrix Quantum Group $GL_{g,h}(2)$ (1997)
Aneva, B. L., Dobrev, V. K., Mihov, S. G.
We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group $GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters and is split in two subalgebras: $U'_{g,h}$...