Study of formality for the Heisenberg algebra

In this paper, we compute the Chevalley-Eilenberg cohomology of the three-dimensionnal Heisenberg Lie algebra with values in its universal enveloping algebra. We also compte the Schouten brackets on cochains and cohomology level in order to write the formality equations. It turns out that there is no formality, ans that the perturbed L-infinity structure on the cohomology has non-trivial terms in infinitely manu degrees.Comment: 15 page

Brackets with (τ,σ)(\tau,\sigma)-derivations and (p,q)(p,q)-deformations of Witt and Virasoro algebras

The aim of this paper is to study some brackets defined on $(\tau,\sigma)$-derivations satisfying quasi-Lie identities. Moreover, we provide examples of $(p,q)$-deformations of Witt and Virasoro algebras as well as $\mathfrak{sl}(2)$ algebra. These constructions generalize the results obtained by Hartwig, Larsson and Silvestrov on $\sigma$-derivations, arising in connection with discretizations and deformations of algebras of vector fields.Comment: 30 page

DISCUSSION ON THE COMPOSITION AND TRANSPORT COEFFICIENTS CALCULATION MADE IN PLASMA OUT OF EQUILIBRIUM

International audienceIn this paper, the composition calculation in plasma out of thermal equilibrium is discussed and we test the viscosity formulations of Wilke, Gupta et al, Chapman Enskog and Sutherland in air plasma out of thermal equilibrium. Finally we applied the formulations to Fire II reentry

Formalité liée aux algèbres enveloppantes et étude des algèbres Hom-(co)Poisson

Le but de cette thèse est d'étudier quelques aspects algébriques du problème de quantification par déformation. On considère d'une part la formalité dans le cas des algèbres libres et de l'algèbre de Lie so(3), et on s'intéresse d'autre part à la quantification par déformation pour des structures Hom-algébriques. Suivant le résultat de formalité de Kontsevich en 1997 pour les algèbres symétriques, on étudie dans la première partie de cette thèse les algèbres libres, qui sont un cas particulier d'algèbres enveloppantes, et on montre qu'il n'y a pas formalité en général, sauf dans les cas triviaux. On montre aussi qu'il n'y a pas formalité pour l'algèbre de Lie so(3). Les techniques utilisées sont de type homologiques. On calcule la cohomologie de ces algèbres et on procède à la construction du L-infini-quasi-isomorphisme entre l'algèbre de Lie différentielle graduée des cochaînes de Hochschild munie du crochet de Gerstenhaber et l'algèbre de la cohomologie munie du crochet de Schouten. Dans la seconde partie de ce travail, on utilise un principe de déformation par twist pour les structures Hom-algébriques, pour construire de nouvelles structures de même type, ou encore pour déformer une structure classique en une Hom-structure correspondante à l'aide d'un morphisme d'algèbres. En particulier, on applique ce procédé aux structures de Poisson et aux star-produits de Moyal-Weyl. Par ailleurs, on établit une correspondance entre les algèbres enveloppantes d'algèbres Hom-Lie possédant une structure Hom-coPoisson et les bigèbres Hom-Lie.This thesis aims to study some algebraic aspects of the deformation quantization problem. On one hand, we consider formality for free algebras and the Lie algebra so(3), and on the other hand we study deformation quantization for Hom-algebraic structures. Following Kontsevich's formality result in 1997 for symmetric algebras, we study in the first part free algebras, which are a particular case of envelopping algebras, and show that there is no formality, except for the trivial cases. We also show that there is no formality for the Lie algebra so(3). The tools used are homological ones. We compute the cohomology of these algebras and proceed to the construction of the L-infinity-quasi-isomorphism between the differential graded Lie algebra of the Hochschild cochains endowed with the Gerstenhaber bracket and the cohomology algebra endowed with the Schouten bracket. In the second part of this work, we use a principle of deformation by twist for Hom-algebraic structures, to construct new structures of the same type, or to deform a classical structure in the corresponding Hom-structure using an algebra morphism. In particular, we apply this method to Poisson structures and Moyal-Weyl star-products. Besides, we establish a correspondance between enveloping algebras of Hom-Lie algebras endowed with a Hom-coPoisson structure and Hom-Lie bialgebras.MULHOUSE-SCD Sciences (682242102) / SudocSudocFranceF

Financing Strategies for Municipal Energy Efficiency

Energy efficiency represents a significant opportunity to reduce energy use, save money and reduce environmental impacts. For municipalities that are facing increasingly tight budgets and have an aging building stock, efficiency represents an especially attractive opportunity. One of the key challenges, however, is how to consistently secure the initial capital necessary to make investments in projects that increase efficiency. Based on a partnership with the Clean Energy Coalition in administering a $4.4 million grant for Michigan‘s Cities of Promise, this report details how revolving energy funds can assist cities by offering a sustainable source of capital to invest in energy efficiency projects. In addition, this report discusses best practices and lessons learned in implementing the Cities of Promise project. Finally, this report evaluates two different fund structures: a fully grant-based fund, and an L3C-based fund that could combine grants with investor capital.Master of ScienceNatural Resources and EnvironmentUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/83535/1/Financing Strategies for Municipal Energy Efficiency.pd