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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2002.01875 |
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Table of Contents:
- Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. 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 $\mathbb{R}_{>0}$-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.