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Induced representation theories between equivalent Fell bundles

Volume 273 / 2023

Weijiao He Studia Mathematica 273 (2023), 239-267 MSC: Primary 47L55 DOI: 10.4064/sm230218-3-8 Published online: 7 December 2023


We construct a tool consisting of three theorems revealing the connection of the induced representation theories between two equivalent Fell bundles, with the aid of which we may transfer induced representation-theoretic theorems for saturated Fell bundles to arbitrary Fell bundles. Letting $G$ be a locally compact group with closed subgroup $H$ and $\mathscr {B}$ a Fell bundle over $G$, as applications of our main result we prove that any $\ast $-representation of the restricted bundle $\mathscr {B}_H$ can be induced to $\mathscr {B}$; and we show that $C^{\ast }(\mathscr {B}_H)$ and $C^{\ast }(\mathscr {D})$, where $\mathscr {D}$ is the $G, G/H$ transformation bundle derived from $\mathscr {B}$, are Morita equivalent if and only if $C^{\ast }(\mathscr {B}_H)$ and $C^{\ast }(\mathscr {B}_{xHx^{-1}})$ are Morita equivalent for any $x \in G$.


  • Weijiao HeDepartment of Mathematics and Statistics
    Taiyuan Normal University
    Jinzhong 030619, Shanxi, China

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