arXiv subjects
Publications and source records attributed to Paulo Antunes.
We show that split Courant algebroids, i.e., those defined on a Whitney sum $A \oplus A^*$, are in a one-to-one correspondence with multiplicative curved $L_\infty$-algebras. This one-to-one correspondence extends to Nijenhuis morphisms and behaves well under the operation of twisting by a bivector.
The BIOSTIRLING - 4SKA (B4S) is a EU demonstration project dealing with the implementation of a cost-effective and efficient new generation of solar dish-Stirling plants based on hybridization and efficient storage at the industrial scale. The main goal of the B4S demonstration project is the generation of electric power using simultaneously solar power and gas to supply an isolated system and act as a scalable example of potential power supply for many infrastructures, including future sustainable large scientific infrastructures. B4S build an interdisciplinary approach to address reliability, maintainability and costs of this technology. In April 2017, B4S successfully tested in Portugal the first world Stirling hybrid system providing about 4kW of power to a phased array of antennas, overcoming challenges in Stirling and hybridization and smartgrid technologies. B4SKA Consortium, with fourteen companies from six European countries, has performed the engineering, construction, assembly and experimental exploitation, under contract signed with the European to develop on off-grid demonstrator in Contenda (Moura) Portugal.
We show that well known structures on Lie algebroids can be viewed as Nijenhuis tensors or pairs of compatible tensors on Courant algebroids. We study compatibility and construct hierarchies of these structures.
We extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nijenhuis, deformation-Nijenhuis and Nijenhuis pairs) that extend to Courant algebroids the notion of a Poisson-Nijenhuis manifold, by using the idea that both the Poisson and the Nijenhuis structures, although they seem to be different in nature when considered on manifolds, are just $(1,1)$-tensors on the usual Courant algebroid $TM \oplus T^*M $ satisfying several constraints. For each of the generalizations mentioned, we show that there are natural hierarchies obtained by successive deformation by one of the $(1,1)$-tensor.
We define the Poisson quasi-Nijenhuis structures with background on Lie algebroids and we prove that to any generalized complex structure on a Courant algebroid which is the double of a Lie algebroid is associated such a structure. We prove that any Lie algebroid with a Poisson quasi-Nijenhuis structure with background constitutes, with its dual, a quasi-Lie bialgebroid. We also prove that any pair $(π,ω)$ of a Poisson bivector and a 2-form induces a Poisson quasi-Nijenhuis structure with background and we observe that particular cases correspond to already known compatibilities between $π$ and $ω$.