Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform

Abstract

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.

26 pages; v1: added a reference, corrected typos; v2: changed title, added a reference, typos fixed

References in corpus (3)

• Deformation Quantization: Twenty Years After
• On Casimir's Ghost
• Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)

Cited by in corpus (7)

• Higher-spin Chern-Simons theories in odd dimensions
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Hochschild cohomology of the Weyl algebra and Vasiliev's equations
• Hochschild Cohomology and Deformations of Clifford-Weyl Algebras
• On Two Theorems About Symplectic Reflection Algebras
• Hochschild Cohomology Theories in White Noise Analysis