1998/05/01 by Denis V. Juriev, Juriev, Denis V.
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.math/9805001
bilingual revised version [English translation+Russian original]: minor corrections
openalex publication_date 1998/05/01 · arxiv created 1998/06/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper there are investigated various approximate representations of the infinite dimensional \Bbb Z--graded Lie algebras: the Witt algebra of all Laurent polynomial vector fields on a circle and its one-dimensional nontrivial central extension, the Virasoro algebra, by the infinite dimensional hidden symmetries in the Verma modules over the Lie algebra \sl(2,C). There are considered as asymptotic representations "mod O(ℏn)" and representations up to a class \frak S of operators (compact operators, Hilbert-Schmidt operators and finite-rank operators) as cases, which combine both types of approximations and in these cases an effect of noncommutativity of the order of their perform is explicated, that perhaps is underlied by a more general fundamental fact of deviations between the asymptotical theory of pseudodifferential operators and the pseudodifferential calculus on the asymptotic manifolds.