### Abstract

We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family script G sign → B of Lie groups (these families are called "gauge-invariant families" in what follows). If the fibers of G → 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 on the bundle script G sign → B. The algebras of invariant pseudodifferential operators that we study, ψ_{inv}^{∞}(Y) and Ψ_{inv}^{∞}(Y), are generalizations of "parameter dependent" algebras of pseudodifferential operators (with parameter in 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.

Original language | English (US) |
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Pages (from-to) | 155-183 |

Number of pages | 29 |

Journal | Acta Mathematica Hungarica |

Volume | 99 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Acta Mathematica Hungarica*,

*99*(1-2), 155-183. https://doi.org/10.1023/A:1024517714643

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*Acta Mathematica Hungarica*, vol. 99, no. 1-2, pp. 155-183. https://doi.org/10.1023/A:1024517714643

**An index theorem for gauge-invariant families : The case of solvable groups.** / Nistor, Victor.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An index theorem for gauge-invariant families

T2 - The case of solvable groups

AU - Nistor, Victor

PY - 2003/4/1

Y1 - 2003/4/1

N2 - We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family script G sign → B of Lie groups (these families are called "gauge-invariant families" in what follows). If the fibers of G → 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 on the bundle script G sign → B. The algebras of invariant pseudodifferential operators that we study, ψinv∞(Y) and Ψinv∞(Y), are generalizations of "parameter dependent" algebras of pseudodifferential operators (with parameter in Rq). 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.

AB - We define the gauge-equivariant index of a family of elliptic operators invariant with respect to the free action of a family script G sign → B of Lie groups (these families are called "gauge-invariant families" in what follows). If the fibers of G → 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 on the bundle script G sign → B. The algebras of invariant pseudodifferential operators that we study, ψinv∞(Y) and Ψinv∞(Y), are generalizations of "parameter dependent" algebras of pseudodifferential operators (with parameter in Rq). 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.

UR - http://www.scopus.com/inward/record.url?scp=0037396557&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037396557&partnerID=8YFLogxK

U2 - 10.1023/A:1024517714643

DO - 10.1023/A:1024517714643

M3 - Article

AN - SCOPUS:0037396557

VL - 99

SP - 155

EP - 183

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 1-2

ER -