$q$-deformation of Witt-Burnside rings
| dc.creator | Oh, Young-Tak | |
| dc.date | 2004-11-16 | |
| dc.date | 2006-12-20 | |
| dc.date.accessioned | 2026-07-07T07:36:18Z | |
| dc.date.available | 2026-07-07T07:36:18Z | |
| dc.description | 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 A. Dress and C. Siebeneicher (Adv. Math. {70} (1988), 87-132). 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 (1998), 703-732). Finally, we classify $\mathbb W_G^q$ up to strict natural isomorphism in case where $G$ is an abelian profinite group. | |
| dc.description | Some revision was made | |
| dc.identifier | https://arxiv.org/abs/math/0411353 | |
| dc.identifier | http://arxiv.org/abs/math/0411353 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120378 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 11F03,11F22,17B70 | |
| dc.title | $q$-deformation of Witt-Burnside rings | |
| dc.type | text |