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

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.

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

UBVRI observations of the flickering of RS Ophiuchi at Quiescence

We report observations of the flickering variability of the recurrent nova RS Oph at quiescence on the basis of simultaneous observations in 5 bands (UBVRI). RS Oph has flickering source with (U-B)_0=-0.62 \pm 0.07, (B-V)_0=0.15 \pm 0.10, (V-R)_0=0.25 \pm 0.05. We find for the flickering source a temperature T_fl = 9500 \pm 500 K, and luminosity L_fl = 50 - 150 L_sun (using a distance of d=1.6kpc). We also find that on a (U-B) vs (B-V) diagram the flickering of the symbiotic stars differs from that of the cataclysmic variables. The possible source of the flickering is discussed. The data are available upon request from the authors and on the web www.astro.bas.bg/~rz/RSOph.UBVRI.2010.MNRAS.tar.gz.Comment: 7 pages, MNRAS (accepted

Dissecting the long-term emission behaviour of the BL Lac object Mrk 421

We report on long-term multiwavelengthmonitoring of blazar Mrk 421 by the GLAST-AGILE Support Program of the Whole Earth Blazar Telescope (GASP-WEBT) collaboration and Steward Observatory, and by the Swift and Fermi satellites. We study the source behaviour in the period 2007–2015, characterized by several extreme flares. The ratio between the optical, X-ray and γ -ray fluxes is very variable. The γ -ray flux variations show a fair correlation with the optical ones starting from 2012.We analyse spectropolarimetric data and find wavelengthdependence of the polarization degree (P), which is compatible with the presence of the host galaxy, and no wavelength dependence of the electric vector polarization angle (EVPA). Optical polarimetry shows a lack of simple correlation between P and flux and wide rotations of the EVPA.We build broad-band spectral energy distributions with simultaneous near-infrared and optical data from the GASP-WEBT and ultraviolet and X-ray data from the Swift satellite. They show strong variability in both flux and X-ray spectral shape and suggest a shift of the synchrotron peak up to a factor of ∼50 in frequency. The interpretation of the flux and spectral variability is compatible with jet models including at least two emitting regions that can change their orientation with respect to the line of sight.http://10.0.4.69/mnras/stx2185Accepted manuscrip

WEBT multiwavelength monitoring and XMM-Newton observations of BL Lacertae in 2007-2008. Unveiling different emission components

In 2007-2008 we carried out a new multiwavelength campaign of the Whole Earth Blazar Telescope (WEBT) on BL Lacertae, involving three pointings by the XMM-Newton satellite, to study its emission properties. The source was monitored in the optical-to-radio bands by 37 telescopes. The brightness level was relatively low. Some episodes of very fast variability were detected in the optical bands. The X-ray spectra are well fitted by a power law with photon index of about 2 and photoelectric absorption exceeding the Galactic value. However, when taking into account the presence of a molecular cloud on the line of sight, the data are best fitted by a double power law, implying a concave X-ray spectrum. The spectral energy distributions (SEDs) built with simultaneous radio-to-X-ray data at the epochs of the XMM-Newton observations suggest that the peak of the synchrotron emission lies in the near-IR band, and show a prominent UV excess, besides a slight soft-X-ray excess. A comparison with the SEDs corresponding to previous observations with X-ray satellites shows that the X-ray spectrum is extremely variable. We ascribe the UV excess to thermal emission from the accretion disc, and the other broad-band spectral features to the presence of two synchrotron components, with their related SSC emission. We fit the thermal emission with a black body law and the non-thermal components by means of a helical jet model. The fit indicates a disc temperature greater than 20000 K and a luminosity greater than 6 x 10^44 erg/s.Comment: 11 pages, 7 figures, accepted for publication in A&

Duality for Exotic Bialgebras

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 the bialgebras which are in duality with these three exotic matrix bialgebras. We note that the $L-T$ duality of FRT is not sufficient for the construction of the bialgebras in duality. We find also the quantum planes corresponding to these bialgebras both by the Wess-Zumino R-matrix method and by Manin's method.Comment: 25 pages, LaTeX2e, using packages: cite, amsfonts, amsmath, subeq

A new activity phase of the blazar 3C 454.3. Multifrequency observations by the WEBT and XMM-Newton in 2007-2008

We present and analyse the WEBT multifrequency observations of 3C 454.3 in the 2007-2008 observing season, including XMM-Newton observations and near-IR spectroscopic monitoring, and compare the recent emission behaviour with the past one. In the optical band we observed a multi-peak outburst in July-August 2007, and other faster events in November 2007 - February 2008. During these outburst phases, several episodes of intranight variability were detected. A mm outburst was observed starting from mid 2007, whose rising phase was contemporaneous to the optical brightening. A slower flux increase also affected the higher radio frequencies, the flux enhancement disappearing below 8 GHz. The analysis of the optical-radio correlation and time delays, as well as the behaviour of the mm light curve, confirm our previous predictions, suggesting that changes in the jet orientation likely occurred in the last few years. The historical multiwavelength behaviour indicates that a significant variation in the viewing angle may have happened around year 2000. Colour analysis reveals a complex spectral behaviour, which is due to the interplay of different emission components. All the near-IR spectra show a prominent Halpha emission line, whose flux appears nearly constant. The analysis of the XMM-Newton data indicates a correlation between the UV excess and the soft-X-ray excess, which may represent the head and the tail of the big blue bump, respectively. The X-ray flux correlates with the optical flux, suggesting that in the inverse-Compton process either the seed photons are synchrotron photons at IR-optical frequencies or the relativistic electrons are those that produce the optical synchrotron emission. The X-ray radiation would thus be produced in the jet region from where the IR-optical emission comes.Comment: 10 pages, 12 figures (7 included in the text, 5 in GIF format), accepted for publication in A&