q-Deformation of Witt-Burnside rings

초록

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 W-G(q) up to strict natural isomorphism in case where G is an abelian profinite group.

키워드