Maximal ideals in the Lie algebra of vector fields
Modular classes of Q-manifolds: a review and some applications
A Q-manifold is a supermanifold equipped with an odd vector field that squares to zero. The notion of the modular class of a Q-manifold – which is viewed as the obstruction to the existence of a Q-invariant Berezin volume – is not well know. We review the basic ideas and then apply this technology to various examples, including -algebroids and higher Poisson manifolds.
Modular Classes of Q-Manifolds, Part II: Riemannian Structures Odd Killing Vectors Fields
We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds are unimodular, i.e., come equipped with a Q-invariant Berezin volume.
Multiparameter quantum function algebra at roots of 1.
Non-weight modules over the super Schrödinger algebra
We construct a family of non-weight modules which are free -modules of rank 2 over the super Schrödinger algebra in -dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free -modules of rank 2 over are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.
On deformations and contractions of Lie algebras.
On quantum and classical Poisson algebras
Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular a somewhat unexpected fact that the algebras of linear differential operators acting on smooth sections of two real vector bundles of rank 1 are isomorphic as Lie algebras if and only if the base manifolds are diffeomorphic, whether or not the line bundles themselves are isomorphic....
On roots of the automorphism group of a circular domain in
We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.
On the cohomology of vector fields on parallelizable manifolds
In the present paper we determine for each parallelizable smooth compact manifold the second cohomology spaces of the Lie algebra of smooth vector fields on with values in the module . The case of is of particular interest since the gauge algebra of functions on with values in a finite-dimensional simple Lie algebra has the universal central extension with center , generalizing affine Kac-Moody algebras. The second cohomology classifies twists of the semidirect product of with the...
On the geometric prequantization of brackets.
En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.
On the structure of graded transitive Lie algebras.
On the structure of transitively differential algebras.
Projectively equivariant quantization and symbol on supercircle
Let be the space of linear differential operators on weighted densities from to as module over the orthosymplectic Lie superalgebra , where , is the space of tensor densities of degree on the supercircle . We prove the existence and uniqueness of projectively equivariant quantization map from the space of symbols to the space of differential operators. An explicite expression of this map is also given.
Quasi-bigèbres jacobiennes
Remarks on local Lie algebras of pairs of functions
Starting by the famous paper by Kirillov, local Lie algebras of functions over smooth manifolds were studied very intensively by mathematicians and physicists. In the present paper we study local Lie algebras of pairs of functions which generate infinitesimal symmetries of almost-cosymplectic-contact structures of odd dimensional manifolds.
Remarks on the Symmetry lie Algebras of first Integrals of Scalar third Order Ordinary Differential Equation with Maximal Symmetry
R-matrix brackets and their quantization
Schwarzian derivative related to modules of differential operators on a locally projective manifold
We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the same problems...
Schwinger terms, gerbes, and operator residues
Second-order conformally equivariant quantization in dimension .