Pseudo-differential extension for graded nilpotent Lie groups

  • Eske Ewert

    Georg-August-Universität Göttingen, Göttingen, Germany; Leibniz Universität Hannover, Hannover, Germany
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Abstract

Classical pseudo-differential operators of order zero on a graded nilpotent Lie group form a -subalgebra of the bounded operators on . We show that its -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 -action on a certain ideal in the -algebra of the tangent groupoid of . The action takes the graded structure of into account. Our construction allows to compute the -theory of the algebra of symbols.

Cite this article

Eske Ewert, Pseudo-differential extension for graded nilpotent Lie groups. Doc. Math. 28 (2023), no. 6, pp. 1323–1379

DOI 10.4171/DM/940