Abstract
In this paper, we construct a q-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where q ranges over the set of integers. When q = 1, it coincides with the Witt-Burnside ring introduced by Dress and Siebeneicher (Adv. Math. 70, 87–132 (1988)). To achieve our goal we first show that there exists a q-deformation of the necklace ring of a profinite group over a commutative ring. As in the classical case, i.e., the case q = 1, q-deformed Witt-Burnside rings and necklace rings always come equipped with inductions and restrictions. We also study their properties. As a byproduct, we prove a conjecture due to Lenart (J. Algebra. 199, 703-732 (1998)). Finally, we classify \({\mathbb{W}_G^q}\) up to strict natural isomorphism in case where G is an abelian profinite group.
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The author gratefully acknowledges support from the following grants: KOSEF Grant # R01-2003-000-10012-0; KRF Grant # 2006-331-C00011.
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Oh, YT. q-deformation of Witt-Burnside rings. Math. Z. 257, 151–191 (2007). https://doi.org/10.1007/s00209-007-0119-2
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DOI: https://doi.org/10.1007/s00209-007-0119-2