Isomorphisms of Group Algebras | Zendy

Wood G. V. | Zendy

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Isomorphisms of Group Algebras

Author(s) -

Wood G. V.

Publication year - 1983

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/15.3.247

Subject(s) - mathematics , abelian group , isomorphism (crystallography) , group algebra , group (periodic table) , pure mathematics , conjecture , algebra over a field , locally compact group , locally compact space , combinatorics , chemistry , organic chemistry , crystal structure , crystallography

Let G 1 and G 2 be locally compact groups. If T is an algebra isomorphism of L 1 (G 1 ) onto L 1 (G 2 ) with ‖ T ‖ ⩽ ½(1+√3), then G 1 and G 2 are isomorphic. This improves on earlier results, and, in a certain sense, is best possible. However, the main conjecture that the groups are isomorphic if ‖ T ‖ < √2 remains unsolved except for abelian groups and for connected groups. Similar results are given for the measure algebra M ( G ) and for the algebra C ( G ) of continuous functions when the group G is compact.

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