ON SPECIALITY OF BINARY-LIE ALGEBRAS

In the present work, binary-Lie, assocyclic, and binary (-1,1) algebras are studied. We prove that, for every assocyclic algebra A, the algebra A(-) is binary-Lie. We find a simple non-Malcev binary-Lie superalgebra T that cannot be embedded in A(-s) for an assocyclic superalgebra A. We use the Grassmann envelope of T to prove the similar result for algebras. This solve negatively a problem by Filippov (see [1, Problem 2.108]). Finally, we prove that the superalgebra T is isomorphic to the commutator superalgebra A(-s) for a simple binary (-1,1) superalgebra A.

Braided m-Lie algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End(F)M, where M is a Yetter-Drinfeld module over B with dimB < infinity. In particular, generalized classical braided m-Lie algebras sl(q,f)(GM(G)(A),F) and osp(q,l)(GM(G)(A),M,F) of generalized matrix algebra GMG(A) are constructed and their connection with special generalized matrix Lie superalgebra sl(s,f)(GM(Z2)(A(s)),F) and orthosymplectic generalized matrix Lie super algebra osp(s,l) (GM(Z2)(A(s)),M-s,F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.

On super-RS algebra and Drinfeld realization of quantum affine superalgebras

We describe the realization of the super-Reshetikhin-Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U-q [osp(1/2)((1))] and its degeneration - central extended super-Yangian double DY(h over bar) [osp(1/2)((1))].

CURRENT-ALGEBRA OF SUPER WZNW MODELS

We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super-affine Lie algebras as expected, but, in general, them are intertwining fields connecting both right and left sectors, analogously to the bosonic case. Moreover, in the present supersymmetric extension we have a quadratic algebra, rather than an affine Lie algebra, due to the mixing between bosonic and fermionic fields; the purely fermionic sector displays an affine Lie algebra as well.

Higher spin constraints and the super (W∞/2 ⊕ W1+∞/2) algebra in the super eigenvalue model

We show that the partition function of the super eigenvalue model satisfies, for finite N (non-perturbatively), an infinite set of constraints with even spins s = 4, 6, . . . , ∞. These constraints are associated with half of the bosonic generators of the super (W∞/2 ⊕ W1+∞/2) algebra. The simplest constraint (s = 4) is shown to be reducible to the super Virasoro constraints, previously used to construct the model.

Comments on the Drinfeld realization of the quantum affine superalgebra U-q[gl(m backslash n)(1)] and its Hopf algebra structure

By generalizing the Reshetikhin and Semenov-Tian-Shansky construction to supersymmetric cases, we obtain the Drinfeld current realization for the quantum affine superalgebra U-q[gl(m\n)((1))]. We find a simple coproduct for the quantum current generators and establish the Hopf algebra structure of this super current algebra.

Coefficients de Clebsch-Gordan de la super-algèbre osp(1|2)

Les fonctions génératrices des coefficients de Clebsch Gordan pour la superalgèbre de Lie osp(1|2) sont dérivées en utilisant deux approches. Une première approche généralise une méthode proposée par Granovskii et Zhedanov pour l'appliquer dans le cas de osp(1|2), une algèbre dont le coproduit est torsadé. Une seconde approche repose sur la réalisation de osp(1|2) en tant qu'algèbre dynamique d'un oscillateur parabosonique et utilise une équivalence dans cette réalisation entre le changements de coordonnées polaires à cartésiennes et le problème de Clebsch-Gordan. Un chapitre moins formel précède ces dérivations et présente comment le problème de Clebsch-Gordan s'interprète en tant que réalisation d'une algèbre de fusion. La notion abstraite de fusion est introduite, soulignant son importance en physique, pour en venir au cas particulier du problème de Clebsch-Gordan. Un survol du cas de l'algèbre osp(1|2) et de ses utilisations en physique mathématique conclut ce chapitre.

Integrablility of a classical N=2 super sinh-Gordon model with jump defects

The Lagrangian formalism for the N = 2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is given and an one-soliton solution is obtained.The Lax formulation based on the affine super Lie algebra sl(2, 2) within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.

SUPERSYMMETRIC CONSTRUCTION OF W-ALGEBRAS FROM SUPER TODA AND WZNW THEORIES

A systematic construction of super W algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy momentum tensor, is discussed in general terms for all super Lie algebras whose simple roots are fermionic. A detailed discussion employing the Dirac bracket structure and an explicit construction of W algebras for the cases of OSP(1, 2), OSP(2, 2), OSP(3, 2) and D(2, 1\ alpha) are given. The N = 1 and N = 2 superconformal algebras are discussed in the pertinent cases.

Classical and quantum N = 1 super W∞-algebras

We construct higher-spin N = 1 superalgebras as extensions of the super-Virasoro algebra containing generators for all spins s ≥ 3/2. We find two distinct classical (Poisson) algebras on the phase superspace. Our results indicate that only one of them can be consistently quantized.

On the mass determination of super-Earths orbiting active stars: the CoRoT-7 system

Context. Star activity makes the mass determination of CoRoT-7b and CoRoT 7c uncertain. Investigators of the CoRoT team proposed several solutions, but all but one of them are larger than the initial determinations of 4.8 +/- 0.8 M(Earth) for CoRoT-7b and 8.4 +/- 0.9 M(Earth) for CoRoT 7c. Aims. This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to redetermine the planet masses and to explore techniques for determining mass and orbital elements of planets discovered around active stars when the relative variation in the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. Methods. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009, A&A, 506, 303) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) the approach proposed by Hatzes et al. (2010, A&A, 520, A93) using only those nights in which two or three observations were done; (2) a pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system. The periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2 454 847-873 are used because they include many nights with multiple observations; otherwise, it is not possible to separate the effects of the rotation fourth harmonic (5.91 d = P(rot)/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). Results. The results of the various approaches are combined to give planet mass values 8.0 +/- 1.2 M(Earth) for CoRoT-7b and 13.6 +/- 1.4 M(Earth) for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given. Conclusions. The results obtained with three different approaches agree to give higher masses than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 +/- 3.5 g cm(-3), so CoRoT-7b may be rocky with a large iron core.

Transiting exoplanets from the CoRoT space mission XIII. CoRoT-13b: a dense hot Jupiter in transit around a star with solar metallicity and super-solar lithium content

We announce the discovery of the transiting planet CoRoT-13b. Ground-based follow-up in CFHT and IAC80 confirmed CoRoT's observations. The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope. It is a hot Jupiter-like planet with an orbital period of 4.04 days, 1.3 Jupiter masses, 0.9 Jupiter radii, and a density of 2.34 g cm(-3). It orbits a G0V star with T(eff) = 5 945 K, M(*) = 1.09 M(circle dot), R(*) = 1.01 R(circle dot), solar metallicity, a lithium content of +1.45 dex, and an estimated age of between 0.12 and 3.15 Gyr. The lithium abundance of the star is consistent with its effective temperature, activity level, and age range derived from the stellar analysis. The density of the planet is extreme for its mass, implies that heavy elements are present with a mass of between about 140 and 300 M(circle plus).

Transiting exoplanets from the CoRoT space mission VIII. CoRoT-7b: the first super-Earth with measured radius

Aims. We report the discovery of very shallow (Delta F/F approximate to 3.4 x 10(-4)), periodic dips in the light curve of an active V = 11.7 G9V star observed by the CoRoT satellite, which we interpret as caused by a transiting companion. We describe the 3-colour CoRoT data and complementary ground-based observations that support the planetary nature of the companion. Methods. We used CoRoT colours information, good angular resolution ground-based photometric observations in- and out- of transit, adaptive optics imaging, near-infrared spectroscopy, and preliminary results from radial velocity measurements, to test the diluted eclipsing binary scenarios. The parameters of the host star were derived from optical spectra, which were then combined with the CoRoT light curve to derive parameters of the companion. Results. We examined all conceivable cases of false positives carefully, and all the tests support the planetary hypothesis. Blends with separation >0.40 '' or triple systems are almost excluded with a 8 x 10(-4) risk left. We conclude that, inasmuch we have been exhaustive, we have discovered a planetary companion, named CoRoT-7b, for which we derive a period of 0.853 59 +/- 3 x 10(-5) day and a radius of R(p) = 1.68 +/- 0.09 R(Earth). Analysis of preliminary radial velocity data yields an upper limit of 21 M(Earth) for the companion mass, supporting the finding. Conclusions. CoRoT-7b is very likely the first Super-Earth with a measured radius. This object illustrates what will probably become a common situation with missions such as Kepler, namely the need to establish the planetary origin of transits in the absence of a firm radial velocity detection and mass measurement. The composition of CoRoT-7b remains loosely constrained without a precise mass. A very high surface temperature on its irradiated face, approximate to 1800-2600 K at the substellar point, and a very low one, approximate to 50 K, on its dark face assuming no atmosphere, have been derived.

The CoRoT-7 planetary system: two orbiting super-Earths

We report on an intensive observational campaign carried out with HARPS at the 3.6 m telescope at La Silla on the star CoRoT-7. Additional simultaneous photometric measurements carried out with the Euler Swiss telescope have demonstrated that the observed radial velocity variations are dominated by rotational modulation from cool spots on the stellar surface. Several approaches were used to extract the radial velocity signal of the planet(s) from the stellar activity signal. First, a simple pre-whitening procedure was employed to find and subsequently remove periodic signals from the complex frequency structure of the radial velocity data. The dominant frequency in the power spectrum was found at 23 days, which corresponds to the rotation period of CoRoT-7. The 0.8535 day period of CoRoT-7b planetary candidate was detected with an amplitude of 3.3 m s(-1). Most other frequencies, some with amplitudes larger than the CoRoT-7b signal, are most likely associated with activity. A second approach used harmonic decomposition of the rotational period and up to the first three harmonics to filter out the activity signal from radial velocity variations caused by orbiting planets. After correcting the radial velocity data for activity, two periodic signals are detected: the CoRoT-7b transit period and a second one with a period of 3.69 days and an amplitude of 4 m s(-1). This second signal was also found in the pre-whitening analysis. We attribute the second signal to a second, more remote planet CoRoT-7c. The orbital solution of both planets is compatible with circular orbits. The mass of CoRoT-7b is 4.8 +/- 0.8 (M(circle plus)) and that of CoRoT-7c is 8.4 +/- 0.9 (M(circle plus)), assuming both planets are on coplanar orbits. We also investigated the false positive scenario of a blend by a faint stellar binary, and this may be rejected by the stability of the bisector on a nightly scale. According to their masses both planets belong to the super-Earth planet category. The average density of CoRoT-7b is rho = 5.6 +/- 1.3 g cm(-3), similar to the Earth. The CoRoT-7 planetary system provides us with the first insight into the physical nature of short period super-Earth planets recently detected by radial velocity surveys. These planets may be denser than Neptune and therefore likely made of rocks like the Earth, or a mix of water ice and rocks.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.