Versal deformations of a dirac type differential operator

Document Type

Article

Publication Date

1-1-1999

Abstract

If we are given a smooth differential operator in the variable x ∈ R/2πZ, its normal form, as is well known, is the simplest form obtainable by means of the Diff(S 1)-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(S 1)-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(S 1)-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. © 1999 Taylor & Francis Group, LLC.

Identifier

33846089934 (Scopus)

Publication Title

Journal of Nonlinear Mathematical Physics

External Full Text Location

https://doi.org/10.2991/jnmp.1999.6.3.1

e-ISSN

17760852

ISSN

14029251

First Page

246

Last Page

254

Issue

3

Volume

6

Fund Ref

Akademia Górniczo-Hutnicza im. Stanislawa Staszica

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