Details
| Original language | English |
|---|---|
| Pages (from-to) | 333-383 |
| Number of pages | 51 |
| Journal | Journal of noncommutative geometry |
| Volume | 17 |
| Issue number | 1 |
| Publication status | Published - 2023 |
Abstract
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the corresponding calculus, the principal symbol of an operator is a family of operators acting on certain nilpotent Lie groups. The role of ellipticity as a Fredholm condition is replaced by the Rockland condition on these groups. Our approach allows to understand this in terms of the representations of the corresponding algebra of principal symbols. Moreover, we compute the K-theory of this algebra.
Keywords
- filtered manifolds, generalized fixed point algebras, index theory, Pseudodifferential calculus, Rockland condition, tangent groupoid
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Geometry and Topology
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In: Journal of noncommutative geometry, Vol. 17, No. 1, 2023, p. 333-383.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Pseudodifferential operators on filtered manifolds as generalized fixed points
AU - Ewert, Eske
PY - 2023
Y1 - 2023
N2 - On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the corresponding calculus, the principal symbol of an operator is a family of operators acting on certain nilpotent Lie groups. The role of ellipticity as a Fredholm condition is replaced by the Rockland condition on these groups. Our approach allows to understand this in terms of the representations of the corresponding algebra of principal symbols. Moreover, we compute the K-theory of this algebra.
AB - On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the corresponding calculus, the principal symbol of an operator is a family of operators acting on certain nilpotent Lie groups. The role of ellipticity as a Fredholm condition is replaced by the Rockland condition on these groups. Our approach allows to understand this in terms of the representations of the corresponding algebra of principal symbols. Moreover, we compute the K-theory of this algebra.
KW - filtered manifolds
KW - generalized fixed point algebras
KW - index theory
KW - Pseudodifferential calculus
KW - Rockland condition
KW - tangent groupoid
UR - http://www.scopus.com/inward/record.url?scp=85151085384&partnerID=8YFLogxK
U2 - 10.4171/JNCG/502
DO - 10.4171/JNCG/502
M3 - Article
AN - SCOPUS:85151085384
VL - 17
SP - 333
EP - 383
JO - Journal of noncommutative geometry
JF - Journal of noncommutative geometry
SN - 1661-6952
IS - 1
ER -