Versal Deformations of a Dirac Type Differential Operator

DOI

10.2991/jnmp.1999.6.3.1How to use a DOI?

Abstract

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Anatoliy K. Prykarpatsky
AU  - Denis Blackmore
PY  - 1999
DA  - 1999/08/02
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.1999.6.3.1
DO  - 10.2991/jnmp.1999.6.3.1
ID  - Prykarpatsky1999
ER  -