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.File in questo prodotto:
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