44 research outputs found
Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform
Using the Moyal *-product and orthosymplectic supersymmetry, we construct a
natural non trivial supertrace and an associated non degenerate invariant
supersymmetric bilinear form for the Lie superalgebra structure of the Weyl
algebra. We decompose adjoint and twisted adjoint actions. We define a
renormalized supertrace and a formal inverse Weyl transform in a deformation
quantization framework and develop some examples.Comment: 26 pages; v1: added a reference, corrected typos; v2: changed title,
added a reference, typos fixe
A star-product approach to noncompact quantum groups
Using duality and topological theory of well behaved Hopf algebras (as
defined in [2]) we construct star-product models of non compact quantum groups
from Drinfeld and Reshetikhin standard deformations of enveloping Hopf algebras
of simple Lie algebras. Our star-products act not only on coefficient functions
of finite-dimensional representations, but actually on all
functions, and they exist even for non linear (semi-simple) Lie groups.Comment: 13 page
Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)
We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n)
inspired by Kostant's cohomological interpretation of the classical theorem. We
show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type
super identity if p, q are non zero and conjecture that neither can any other
classical simple Lie superalgebra with the exception of osp(1,2n).Comment: 11 pages, to be published in Letters in Mathematical Physics; added
references, corrected typo
On Two Theorems About Symplectic Reflection Algebras
We give a new proof and an improvement of two Theorems of J. Alev, M.A.
Farinati, T. Lambre and A.L. Solotar : the first one about Hochschild
cohomology spaces of some twisted bimodules of the Weyl algebra W and the
second one about Hochschild cohomology spaces of the smash product G * W (G a
finite subgroup of SP(2n)), and as an application, we then give a new proof of
a Theorem of P. Etingof and V. Ginzburg, which shows that the Symplectic
Reflection Algebras are deformations of G * W (and, in fact, all possible
ones).Comment: corrected typo
On the equivalence between continuous and differential deformation theories
International audienc
Nonlinear multipliers and applications
International audienc
The enveloping algebra of the Lie superalgebra osp(1,2)
International audienc