Decomposing oscillator representations of by a super dual pair
Defining relations for classical Lie superalgebras without Cartan matrices.
Deformations of Batalin-Vilkovisky algebras
We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of a Batalin-Vilkovisky algebra. While such an operator of order 2 defines a Gerstenhaber (Lie) algebra structure on A, an operator of an order higher than 2 (Koszul-Akman definition) leads to the structure of a strongly homotopy Lie algebra (-algebra) on A. This allows us to give a definition of a Batalin-Vilkovisky algebra up to homotopy. We also make a conjecture which is a...
Derivations on the Nijenhuis-Schouten bracket algebra
Derivations on the restricted Nijenhuis-Schouten bracket algebra
Diamonds in thin Lie algebras
In un'algebra di Lie graduata thin, la classe in cui compare il secondo diamante e la caratteristica del campo soggiacente determinano se l'algebra stessa abbia o meno dimensione finita ed in tal caso forniscono anche un limite superiore a tale dimensione.
Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
Dispersive and Strichartz estimates on H-type groups
Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as ) and the Schrödinger equation (decay as ), p being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that p > 1, for the Schrödinger equation.
Divergence operators and odd Poisson brackets
We define the divergence operators on a graded algebra, and we show that, given an odd Poisson bracket on the algebra, the operator that maps an element to the divergence of the hamiltonian derivation that it defines is a generator of the bracket. This is the “odd laplacian”, , of Batalin-Vilkovisky quantization. We then study the generators of odd Poisson brackets on supermanifolds, where divergences of graded vector fields can be defined either in terms of berezinian volumes or of graded connections. Examples...
Durch graduierte Lie-Algebren definierte Paar-Algebren.
Exceptional and orthosymplectic graded Lie algebras
Extension functors of modular Lie algebras.
Fine gradings of low-rank complex Lie algebras and of their real forms.
(Finite) presentations of the Albert-Frank-Shalev Lie algebras
In questo lavoro vengono studiate le algebre di Albert-Frank-Shalev. Queste sono algebre di Lie modulari di dimensione infinita, ottenute da un loop di certe algebre semplici di dimensione finita. Si dimostra che le algebre di Albert-Frank-Shalev sono unicamente determinate, a meno di elementi centrali o secondo centrali, da un certo quoziente finito-dimensionale. Tale risultato si ottiene dando la presentazione finita di un'algebra il cui quoziente sul secondo centro (infinito-dimensionale) è isomorfo...
Finitude de l'homologie de certains modules de dimension finie sur une super algèbre de Lie
Le but de cet article est de formuler une hypothèse permettant d’affirmer que l’homologie d’une super algèbre de Lie à valeurs dans un module de dimension finie est de dimension finie
Formal differential geometry and Nambu-Takhtajan algebra
From Poisson algebras to Gerstenhaber algebras
Constructing an even Poisson algebra from a Gerstenhaber algebra by means of an odd derivation of square 0 is shown to be possible in the category of Loday algebras (algebras with a non-skew-symmetric bracket, generalizing the Lie algebras, heretofore called Leibniz algebras in the literature). Such “derived brackets” give rise to Lie brackets on certain quotient spaces, and also on certain Abelian subalgebras. The construction of these derived brackets explains the origin of the Lie bracket on...
Generalized projective geometries: General theory and equivalance with Jordan structures.
Generic Representations of Classical Lie Superalgebras and Their Localization.
Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.