q-Analog of the Möbius function and the cyclotomic identity associated to a profinite group

• Autores: Young-Tak Oh
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 219, Nº 3, 2008, págs. 852-893
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.06.007
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• Resumen

  • 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.