On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased; author's version of the published pape

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Edades radiométricas de los edificios miocenos de Fuerteventura (Islas Canarias).

Se han realizado once nuevas dataciones K-Ar de las coladas básicas (basaltos, nefelinitas) y sálicas (traquitas) de los tres edificios principales subaéreos (Tetir o Norte, Gran Tarajal o Central y Jandía o Sur) que constituyen la Fase miocena de la isla. Se precisa algo más la cronoestratigrafía relativa entre ellos, así como la correspondiente a los tramos que los integran

Geodetic Study of the 2006–2010 Ground Deformation in La Palma (Canary Islands): Observational Results

La Palma is one of the youngest of the Canary Islands, and historically the most active. The recent activity and unrest in the archipelago, the moderate seismicity observed in 2017 and 2018 and the possibility of catastrophic landslides related to the Cumbre Vieja volcano have made it strongly advisable to ensure a realistic knowledge of the background surface deformation on the island. This will then allow any anomalous deformation related to potential volcanic unrest on the island to be detected by monitoring the surface deformation. We describe here the observation results obtained during the 2006–2010 period using geodetic techniques such as Global Navigation Satellite System (GNSS), Advanced Differential Synthetic Aperture Radar Interferometry (A-DInSAR) and microgravimetry. These results show that, although there are no significant associated variations in gravity, there is a clear surface deformation that is spatially and temporally variable. Our results are discussed from the point of view of the unrest and its implications for the definition of an operational geodetic monitoring system for the island

Invariants of solvable rigid Lie algebras up to dimension 8

The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of fundamental sets of invariants formed by rational functions of the Casimir invariants of the associated nilradical.Comment: 16 pages, 7 table

Detection of volcanic unrest onset in La Palma, Canary Islands, evolution and implications

La Palma island is one of the highest potential risks in the volcanic archipelago of the Canaries and therefore it is important to carry out an in-depth study to define its state of unrest. This has been accomplished through the use of satellite radar observations and an original state-of-the-art interpretation technique. Here we show the detection of the onset of volcanic unrest on La Palma island, most likely decades before a potential eruption. We study its current evolution seeing the spatial and temporal changing nature of activity at this potentially dangerous volcano at unprecedented spatial resolutions and long time scales, providing insights into the dynamic nature of the associated volcanic hazard. The geodetic techniques employed here allow tracking of the fluid migration induced by magma injection at depth and identifying the existence of dislocation sources below Cumbre Vieja volcano which could be associated with a future flank failure. Therefore they should continue being monitored using these and other techniques. The results have implications for the monitoring of steep-sided volcanoes at oceanic islands

Rocas volcánicas submarinas en la base de la Formación Cañadas. Macizo de Tigaiga (N. de Tenerife)

A volcanic submarine formation crops out in the north coast of Tenerife, east of San Juan de la Rambla. This unit is formed by massive and pil/owed lavas, pillow-breccias, hyaloc/astites and palagonitic tuffs and is interpreted as consisUng of subaerial lavas that flowed into shal/ow marine waters. The lavas are amphibolic trachybasalts. An unaltered sample coming fram the most massive zone has yielded a whole rack 2.60±0.17 Ma K-Ar age. These submarine lavas are underlying the oldest formations of the Las Cañadas Series dated at 1.24 Ma in that same area. The submarine lavas correspond to a time period for which very scarce information was yet available in Tenerife

Bell-inequalities for K0K0ˉK^0 \bar{K^0} Pairs from Φ\Phi-Resonance Decays

We analyze the premises of recent propositions to test local realism via Bell-inequalities using neutral kaons from $\Phi$-resonance decays as entangled EPR-pairs. We pay special attention to the derivation of Bell-inequalities, or related expressions, for unstable and oscillating kaon `quasi-spin' states and to the possibility of the actual identification of these states through their associated decay modes. We discuss an indirect method to extract probabilities to find these states by combining experimental information with theoretical input. However, we still find inconsistencies in previous derivations of Bell-inequalities. We show that the identification of the quasi-spin states via their associated decay mode does not allow the free choice to perform different tests on them, a property which is crucial to establish the validity of any Bell-inequality in the context of local realism. In view of this we propose a different kind of Bell-inequality in which the free choice or adjustability of the experimental set-up is guaranteed. We also show that the proposed inequalities are violated by quantum mechanics.Comment: 22 pages. Late