Exotic Bialgebra S03: Representations, Baxterisation and Applications

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 the dual algebra is given in two different parametrisations. The finite-dimensional representations of $s03_F$ are considered. Diagonalisations of the braid matrices are used to yield remarkable insights concerning representations of the L-algebra and to formulate the fusion of finite-dimensional representations. Possible applications are considered, in particular, an exotic eight-vertex model and an integrable spin-chain model.Comment: 24 pages, Latex; V2: revised subsection 4.1, added 9 references, to appear in Annales Henri Poincare in the volume dedicated to D. Arnaudo

Higher Dimensional Multiparameter Unitary and Nonunitary Braid Matrices: Even Dimensions

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 $m_{ij}^{(\pm)}$, $i,j=1,...,n$. For real parameters the matrices $R(\theta)$ are nonunitary. For purely imaginary parameters they became unitary. Thus a unification is achieved with odd dimensional multiparameter solutions presented before.Comment: 07 page

Intranight variability of 3C 454.3 during its 2010 November outburst

Context. 3C 454.3 is a very active flat spectrum radio quasar (blazar) that has undergone a recent outburst in all observed bands, including the optical. Aims. In this work we explore the short-term optical variability of 3C 454.3 during its outburst by searching for time delays between different optical bands. Finding one would be important for understanding the evolution of the spectrum of the relativistic electrons, which generate the synchrotron jet emission. Methods. We performed photometric monitoring of the object by repeating exposures in different optical bands (BVRI). Occasionally, different telescopes were used to monitor the object in the same band to verify the reliability of the smallest variations we observed. Results. Except on one occasion, where we found indications of a lag of the blue wavelengths behind the red ones, the results are inconclusive for most of the other cases. There were either no structures in the light curves to be able to search for patterns, or else different approaches led to different conclusions.Comment: 4 pages, 4 figures. Accepted for publication in A&

On a "New" Deformation of GL(2)

We refute a recent claim in the literature of a "new" quantum deformation of GL(2).Comment: 4 pages, LATE

Nature of Intra-night Optical Variability of BL Lacertae

We present the results of extensive multi-band intra-night optical monitoring of BL Lacertae during 2010--2012. BL Lacertae was very active in this period and showed intense variability in almost all wavelengths. We extensively observed it for a total for 38 nights; on 26 of them observations were done quasi-simultaneously in B, V, R and I bands (totaling 113 light curves), with an average sampling interval of around 8 minutes. BL Lacertae showed significant variations on hour-like timescales in a total of 19 nights in different optical bands. We did not find any evidence for periodicities or characteristic variability time-scales in the light curves. The intranight variability amplitude is generally greater at higher frequencies and decreases as the source flux increases. We found spectral variations in BL Lacertae in the sense that the optical spectrum becomes flatter as the flux increases but in several flaring states deviates from the linear trend suggesting different jet components contributing to the emission at different times.Comment: 12 Pages, 5 figures, 3 Tables, Accepted for Publication in MNRA

Duality and Representations for New Exotic Bialgebras

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 bialgebras S03 and S14 which are not deformations of the of the classical algebras of functions on GL(2) or GL(1|1). With this we finalize the classification of the matrix bialgebras which unital associative algebras generated by four elements. We also find the corresponding dual bialgebras of these new exotic bialgebras and study their representation theory in detail. We also discuss in detail a special case of R_{S1,4} in which the corresponding algebra turns out to be a special case of the two-parameter quantum group deformation GL_{p,q}(2).Comment: 33 pages, LaTeX2e, using packages: cite,amsfonts,amsmath,subeqn; reference updated; v3: corrections in subsection 3.

Short Term Flux and Colour Variations in Low-Energy Peaked Blazars

We have measured multi-band optical flux and colour variations for a sample of 12 low energy peaked blazars on short, day-to-month, timescales. Our sample contains six BL Lacertae objects and six flat spectrum radio quasars. These photometric observations, made during September 2008 to June 2009, used five optical telescopes, one in India and four in Bulgaria. We detected short term flux variations in eleven of these blazars and colour variability in eight of them. Our data indicate that six blazars (3C 66A, AO 0235+164, S5 0716+714, PKS 0735+178, OJ 287 and 3C 454.3) were observed in pre- or post-outburst states, that five (PKS 0420-014, 4C 29.45, 3C 279, PKS 1510-089 and BL Lac) were in a low state, while one (3C 273) was in an essentially steady state. The duty cycles for flux and colour variations on short timescales in these low energy peaked blazars are ~ 92 percent and ~ 33 percent, respectively. The colour vs magnitude correlations seen here support the hypothesis that BL Lac objects tend to become bluer with increase in brightness; however, flat spectrum radio quasars may show the opposite trend, and there are exceptions to these trends in both categories of blazar. We briefly discuss emission models for active galactic nuclei that might explain our results.Comment: 34 pages, 5 tables, 15 figures, accepted for publication in MNRA

Duality for the Jordanian Matrix Quantum Group GLg,h(2)GL_{g,h}(2)

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: $U'_{g,h}$ (with three generators) and $U(Z)$ (with one generator). The subalgebra $U(Z)$ is a central Hopf subalgebra of $U_{g,h}$. The subalgebra $U'_{g,h}$ is not a Hopf subalgebra and its coalgebra structure depends on both parameters. We discuss also two one-parameter special cases: $g =h$ and $g=-h$. The subalgebra $U'_{h,h}$ is a Hopf algebra and coincides with the algebra introduced by Ohn as the dual of $SL_h(2)$. The subalgebra $U'_{-h,h}$ is isomorphic to $U(sl(2))$ as an algebra but has a nontrivial coalgebra structure and again is not a Hopf subalgebra of $U_{-h,h}$.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC nonlinear ma