Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure

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

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

Shallow structure beneath the Central Volcanic Complex of Tenerife from new gravity data: implications for its evolution and recent reactivation

We present a new local Bouguer anomaly map of the Central Volcanic Complex (CVC) of Tenerife, Spain, constructed from the amalgamation of 323 new high precision gravity measurements with existing gravity data from 361 observations. The new anomaly map images the high-density core of the CVC and the pronounced gravity low centred in the Las Cañadas caldera in greater detail than previously available. Mathematical construction of a sub-surface model from the local anomaly data, employing a 3D inversion based on 'growing' the sub-surface density distribution via the aggregation of cells, enables mapping of the shallow structure beneath the complex, giving unprecedented insights into the sub-surface architecture. We find the resultant density distribution in agreement with geological and other geophysical data. The modelled sub-surface structure supports a vertical collapse origin of the caldera, and maps the headwall of the ca. 180 ka Icod landslide, which appears to lie buried beneath the Pico Viejo–Pico Teide stratovolcanic complex. The results allow us to put into context the recorded ground deformation and gravity changes at the CVC during its reactivation in spring 2004 in relation to its dominant structural building blocks. For example, the areas undergoing the most significant changes at depth in recent years are underlain by low-density material and are aligned along long-standing structural entities, which have shaped this volcanic ocean island over the past few million years

Invariants of Triangular Lie Algebras

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], developed further in [J. Phys. A: Math. Theor., 2007, V.40, 113; math-ph/0606045], is used to determine the invariants. A conjecture of [J. Phys. A: Math. Gen., 2001, V.34, 9085], concerning the number of independent invariants and their form, is corroborated.Comment: LaTeX2e, 16 pages; misprints are corrected, some proofs are extende

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