Vol. 54, No. 1, 1974

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Certain representations of infinite group algebras

Indranand Sinha

Vol. 54 (1974), No. 1, 261–267

For any group G, let ρ be an irreducible representation of the group algebra FG over a field F. Then by Schur’s lemma, the center Δ of its commuting ring, is a field containing F. If ρ is finite-dimensional over Δ, lhen it is called finite and if it is finite-dimensional over F itself, then it is called strongly finite. In this paper, certain conditions are given for finiteness of ρ. Also it is shown that for some types of groups, finiteness of ρ is related to the existence of abelian subgroups of finite index in certain quotient of the group. Conditions under which finiteness and strongly finiteness are equivalent, are given. Finally, consequencesof ρ being faithful on G, or being faithful on FG, are studied.

Mathematical Subject Classification
Primary: 16A26
Received: 18 April 1973
Revised: 16 October 1973
Published: 1 September 1974
Indranand Sinha