An index theorem for gauge-invariant families: The case of solvable groups
| dc.creator | Nistor, Victor | |
| dc.date | 2002-01-21 | |
| dc.date.accessioned | 2026-07-07T04:46:00Z | |
| dc.date.available | 2026-07-07T04:46:00Z | |
| dc.description | We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family $\GR \to B$ of Lie groups (these families are called ``gauge-invariant families'' in what follows). If the fibers of $\GR \to B$ 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 about the bundle $\GR \to B$. The algebras of invariant pseudodifferential operators that we study, $\Psm {\infty}Y$ and $\PsS {\infty}Y$, are generalizations of ``parameter dependent'' algebras of pseudodifferential operators (with parameter in $\mathbb R^q$), 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. | |
| dc.description | 23 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0201196 | |
| dc.identifier | http://arxiv.org/abs/math/0201196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63167 | |
| dc.subject | K-Theory and Homology | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Operator Algebras | |
| dc.title | An index theorem for gauge-invariant families: The case of solvable groups | |
| dc.type | text |