Details
| Original language | English |
|---|---|
| Pages (from-to) | 1323-1379 |
| Number of pages | 57 |
| Journal | Documenta mathematica |
| Volume | 28 |
| Issue number | 6 |
| Publication status | Published - 29 Nov 2023 |
Abstract
Classical pseudo-differential operators of order zero on a graded nilpotent Lie group G form a*-subalgebra of the bounded operators on L2 (G). We show that its C*-closure is an extension of a noncommutative algebra of principal symbols by compact operators. As a new approach, we use the generalized fixed point algebra of an R>0-action on a certain ideal in the C*-algebra of the tangent groupoid of G. The action takes the graded structure of G into account. Our construction allows to compute the K-theory of the algebra of symbols.
Keywords
- generalized fixed point algebras, graded Lie groups, homogeneous Lie groups, K-theory, Pseudo-differential calculus, representation theory, tangent groupoid
ASJC Scopus subject areas
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In: Documenta mathematica, Vol. 28, No. 6, 29.11.2023, p. 1323-1379.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Pseudo-differential extension for graded nilpotent Lie groups
AU - Ewert, Eske
N1 - Funding Information: This research was supported by the RTG 2491 “Fourier Analysis and Spectral
PY - 2023/11/29
Y1 - 2023/11/29
N2 - Classical pseudo-differential operators of order zero on a graded nilpotent Lie group G form a*-subalgebra of the bounded operators on L2 (G). We show that its C*-closure is an extension of a noncommutative algebra of principal symbols by compact operators. As a new approach, we use the generalized fixed point algebra of an R>0-action on a certain ideal in the C*-algebra of the tangent groupoid of G. The action takes the graded structure of G into account. Our construction allows to compute the K-theory of the algebra of symbols.
AB - Classical pseudo-differential operators of order zero on a graded nilpotent Lie group G form a*-subalgebra of the bounded operators on L2 (G). We show that its C*-closure is an extension of a noncommutative algebra of principal symbols by compact operators. As a new approach, we use the generalized fixed point algebra of an R>0-action on a certain ideal in the C*-algebra of the tangent groupoid of G. The action takes the graded structure of G into account. Our construction allows to compute the K-theory of the algebra of symbols.
KW - generalized fixed point algebras
KW - graded Lie groups
KW - homogeneous Lie groups
KW - K-theory
KW - Pseudo-differential calculus
KW - representation theory
KW - tangent groupoid
UR - http://www.scopus.com/inward/record.url?scp=85178395405&partnerID=8YFLogxK
U2 - 10.4171/DM/940
DO - 10.4171/DM/940
M3 - Article
AN - SCOPUS:85178395405
VL - 28
SP - 1323
EP - 1379
JO - Documenta mathematica
JF - Documenta mathematica
SN - 1431-0635
IS - 6
ER -