Abstract: This paper reviews the properties and applications of certain n-ary generalizations of Lie algebras in a self-contained and unified way. These generalizations are algebraic structures in which the two-entry Lie bracket has been replaced by a bracket with n entries. Each type of n-ary bracket satisfies a specific characteristic identity which plays the role of the Jacobi identity for Lie algebras. Particular attention will be paid to generalized Lie algebras, which are defined by even multibrackets obtained by antisymmetrizing the associative products of its n components and that satisfy the generalized Jacobi identity, and to Filippov (or n-Lie) algebras, which are defined by fully antisymmetric n-brackets that satisfy the Filippov identity. 3-Lie algebras have surfaced recently in multi-brane theory in the context of the Bagger-Lambert-Gustavsson model. As a result, Filippov algebras will be discussed at length, including the cohomology complexes that govern their central extensions and their deformations ( it turns out that Whitehead's lemma extends to all semisimple n-Lie algebras). When the skewsymmetry of the Lie or n-Lie algebra bracket is relaxed, one is led to a more general type of n-algebras, the n-Leibniz algebras. These will be discussed as well, since they underlie the cohomological properties of n-Lie algebras. The standard Poisson structure may also be extended to the n-ary case. We shall review here the even generalized Poisson structures, whose generalized Jacobi identity reproduces the pattern of the generalized Lie algebras, and the Nambu-Poisson structures, which satisfy the Filippov identity and determine Filippov algebras. Finally, the recent work of Bagger-Lambert and Gustavsson on superconformal Chern-Simons theory will be briefly discussed. Emphasis will be made on the appearance of the 3-Lie algebra structure and on why the A(4) model may be formulated in terms of an ordinary Lie algebra, and on its Nambu bracket generalization.

Abstract: We report an analysis of charmless hadronic decays of neutral B mesons to the final state (KSK +/-)-K-0 pi(-/+) (sic), using a data sample of (465 +/- 5) x 10(6) B (B) over bar events collected with the BABAR detector at the Gamma(4S) resonance. We observe an excess of signal events with a significance of 5.2 standard deviations including systematic uncertainties and measure the branching fraction to be B(B-0 -> (KSK +/-)-K-0 pi(-/+) (sic) (3.2 +/- 0.5 +/- 0.3) x 10(-6), where the uncertainties are statistical and systematic, respectively.

Abstract: The development of highly segmented germanium detectors as well as the algorithms to identify the position of the interaction within the crystal opens the possibility to locate the gamma-ray source using Compton imaging algorithms. While the Compton-suppression shield, coupled to the germanium detector in conventional arrays, works also as an active filter against the gamma rays originated outside the target, the new generation of position sensitive gamma-ray detector arrays has to fully rely on tracking capabilities for this purpose. In specific experimental conditions, as the ones foreseen at radioactive beam facilities, the ability to discriminate background radiation improves the sensitivity of the gamma spectrometer. In this work we present the results of a measurement performed at the Laboratori Nazionali di Legnaro (LNL) aiming the evaluation of the AGATA detector capabilities to discriminate the origin of the gamma rays on an event-by-event basis. It will be shown that, exploiting the Compton scattering formula, it is possible to track back gamma rays coming from different positions, assigning them to specific emitting locations. These imaging capabilities are quantified for a single crystal AGATA detector.