Geodesic
Pseudo-differential extension for graded nilpotent Lie groups
Documenta mathematica, Tome 28 (2023) no. 6, pp. 1323-1379

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/dm/940
Classification : 47G30, 22D25, 46L99, 19K99, 22E25, 35R03
Mots-clés : pseudo-differential calculus, graded Lie groups, homogeneous Lie groups, generalized fixed point algebras, K-theory, tangent groupoid, representation theory 
@article{10_4171_dm_940,
     author = {Eske Ewert},
     title = {Pseudo-differential extension for graded nilpotent {Lie} groups},
     journal = {Documenta mathematica},
     pages = {1323--1379},
     publisher = {mathdoc},
     volume = {28},
     number = {6},
     year = {2023},
     doi = {10.4171/dm/940},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/940/}
}
TY  - JOUR
AU  - Eske Ewert
TI  - Pseudo-differential extension for graded nilpotent Lie groups
JO  - Documenta mathematica
PY  - 2023
SP  - 1323
EP  - 1379
VL  - 28
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/940/
DO  - 10.4171/dm/940
ID  - 10_4171_dm_940
ER  - 
%0 Journal Article
%A Eske Ewert
%T Pseudo-differential extension for graded nilpotent Lie groups
%J Documenta mathematica
%D 2023
%P 1323-1379
%V 28
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/940/
%R 10.4171/dm/940
%F 10_4171_dm_940
Eske Ewert. Pseudo-differential extension for graded nilpotent Lie groups. Documenta mathematica, Tome 28 (2023) no. 6, pp. 1323-1379. doi: 10.4171/dm/940

Cité par Sources :