q-Analog of the Möbius function and the cyclotomic identity associated to a profinite group |
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Authors: | Young-Tak Oh |
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Institution: | Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea |
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Abstract: | Let G be a profinite group and q an indeterminate. In this paper, we introduce and study a q-analog of the Möbius function and the cyclotomic identity arising from the lattice of open subgroups of G. When q is any integer, we show that they have close connections with the functors , , and introduced in Y.-T. Oh, q-Deformation of Witt-Burnside rings, Math. Z. 257 (2007) 151-191]. In particular, we interpret the multiplicative property of the inverse of the table of marks and the Möbius function of G as a composition property of certain functors. Classification of , , and up to strict natural isomorphism as q varies over the set of integers and its application will be dealt with, too. |
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Keywords: | 11F03 1F22 7B70 |
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