Neeb KH, Salmasian H (2016)
Publication Type: Journal article
Publication year: 2016
Book Volume: 282
Pages Range: 213-232
Journal Issue: 1
URI: https://arxiv.org/abs/1506.01558
For every finite dimensional Lie supergroup (G,g), we define a C∗-algebra A:=A(G,g) and show that there exists a canonical bijective correspondence between unitary representations of (G,g) and nondegenerate ∗-representations of A
. The proof of existence of such a correspondence relies on a subtle characterization of smoothing operators of unitary representations previously studied by Neeb, Salmasian, and Zellner.
For a broad class of Lie supergroups, which includes nilpotent as well as classical simple ones, we prove that the associated C∗
-algebra is CCR. In particular, we obtain the uniqueness of direct integral decomposition for unitary representations of these Lie supergroups.
APA:
Neeb, K.H., & Salmasian, H. (2016). Crossed product algebras and direct integral decomposition for Lie supergroups. Pacific Journal of Mathematics, 282(1), 213-232. https://dx.doi.org/10.2140/pjm.2016.282.213
MLA:
Neeb, Karl Hermann, and Hadi Salmasian. "Crossed product algebras and direct integral decomposition for Lie supergroups." Pacific Journal of Mathematics 282.1 (2016): 213-232.
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