Automatic surjectivity of ring homomorphisms on 𝐻*-algebras and algebraic differences among some group algebras of compact groups

Molnár, Lajos

doi:10.1090/S0002-9939-99-04974-6

Automatic surjectivity of ring homomorphisms on $H^*$-algebras and algebraic differences among some group algebras of compact groups
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Proc. Amer. Math. Soc. 128 (2000), 125-134 Request permission

Abstract:

In this paper we present two automatic surjectivity results concerning ring homomorphisms between $p$-classes of an $H^{*}$-algebra which, in some sense, improve the main theorem in a recent paper by the author (Proc. Amer. Math. Soc. 124 (1996), 169–175) quite significantly. Furthermore, we apply our results to show that for arbitrary infinite compact groups $G,G’$, no quotient ring of $L^{2}(G)$ is isomorphic to $L^{p}(G’)$ $(2<p\leq \infty )$, a statement we conjecture to be true for every pair $L^{p}(G), L^{q}(G’)$ of group rings corresponding to different exponents $1\leq p,q\leq \infty$.

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