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- Title
An index theorem for gauge-invariant families: The case of solvable groups.
- Authors
Nistor, V.
- Abstract
We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family <MATH>\cG \to B</MATH> of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers of <MATH>\cG \to B</MATH> are simply-connected and solvable, we compute the Chern character of the gauge-equivariant index, the result being given by an Atiyah–Singer type formula that incorporates also topological information on the bundle <MATH>\cG \to B</MATH>. The algebras of invariant pseudodifferential operators that we study, <MATH>\Psm {\infty}Y</MATH> and <MATH>\PsS {\infty}Y</MATH>, are generalizations of ``parameter dependent'' algebras of pseudodifferential operators (with parameter in <MATH>\bR^q</MATH>), so our results provide also an index theorem for elliptic, parameter dependent pseudodifferential operators. We apply these results to study Fredholm boundary conditions on a simplex.
- Subjects
ELLIPTIC operators; PARTIAL differential operators; DIFFERENTIAL operators; HYPOELLIPTIC operators; PARABOLIC operators; MATHEMATICS
- Publication
Acta Mathematica Hungarica, 2003, Vol 99, Issue 1/2, p155
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1023/A:1024517714643