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| Main Author: | |
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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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| _version_ | 1866912182362439680 |
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| author | Ewert, Eske |
| author_facet | Ewert, Eske |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_01875 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Pseudo-differential extension for graded nilpotent Lie groups Ewert, Eske Operator Algebras 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. |
| title | Pseudo-differential extension for graded nilpotent Lie groups |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2002.01875 |