We introduce and investigate the notion of a quasi-complete group. A group G is quasi-complete if every automorphism phi is an element of Aut(G), with the property that pi and pi circle phi are unitarily equivalent for every unitary irreducible representation p of G, is an inner automorphism of G. Our main result is that every connected linear real reductive Lie group is quasi- complete.

Conti, R., D'Antoni, C., Geatti, L. (2004). Group automorphisms preserving equivalence classes of unitary representations. FORUM MATHEMATICUM, 16(4), 483-503.

Group automorphisms preserving equivalence classes of unitary representations

D'ANTONI, CLAUDIO;GEATTI, LAURA
2004-01-01

Abstract

We introduce and investigate the notion of a quasi-complete group. A group G is quasi-complete if every automorphism phi is an element of Aut(G), with the property that pi and pi circle phi are unitarily equivalent for every unitary irreducible representation p of G, is an inner automorphism of G. Our main result is that every connected linear real reductive Lie group is quasi- complete.
2004
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - GEOMETRIA
English
PRINCIPAL SERIES; COMPACT-GROUPS; GENERATORS; ALGEBRAS
Conti, R., D'Antoni, C., Geatti, L. (2004). Group automorphisms preserving equivalence classes of unitary representations. FORUM MATHEMATICUM, 16(4), 483-503.
Conti, R; D'Antoni, C; Geatti, L
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/31690
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