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ISSN : 1226-0657

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Vol.6 No.1
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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
1999, v.6 no.1, pp.1-8
Lee, Jung-Rye
Lee,, J. (1999). . Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 6(1), 1-8.
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Abstract

Let <TEX>$K_{\alpha}(G)$</TEX> (resp. <TEX>$K_s(G)$</TEX>) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of <TEX>$K_{\alpha}(G)$</TEX> (resp. <TEX>$K_s(G)$</TEX>). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of <TEX>$K_{\alpha}(G)$</TEX> (resp. <TEX>$K_s(G)$</TEX>).

keywords
Kac algebra, sub-Kac algebra, reduced Kac algebra

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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