Volume 6, Issue 3, August 1995, Pages 246 - 254
Versal Deformations of a Dirac Type Differential Operator
Anatoliy K. PRYKARPATSKY, Denis BLACKMORE
Anatoliy K. PRYKARPATSKY
Available Online 1 August 1995.
- https://doi.org/10.2991/jnmp.19188.8.131.52How to use a DOI?
- If we are given a smooth differential operator in the variable x R/2Z, its normal form, as is well known, is the simplest form obtainable by means of the Diff(S1 )-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced Diff(S1 )-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced Diff(S1 )-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters.
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Cite this article
TY - JOUR AU - Anatoliy K. PRYKARPATSKY AU - Denis BLACKMORE PY - 1995 DA - 1995/08 TI - Versal Deformations of a Dirac Type Differential Operator JO - Journal of Nonlinear Mathematical Physics SP - 246 EP - 254 VL - 6 IS - 3 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.19184.108.40.206 DO - https://doi.org/10.2991/jnmp.19220.127.116.11 ID - PRYKARPATSKY1995 ER -