20 06 q - DEFORMATION OF WITT - BURNSIDE RINGS
نویسنده
چکیده
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 ring of integers. When q = 1, this 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 Lenart's conjecture appeared in (J. Algebra. 199 (1998), 703-732). Finally, we provide a necessary and sufficient condition of A so that W q G (A) and W r G (A) be strictly-isomorphic to each other in case where G is an abelian profinite group.
منابع مشابه
. R A ] 1 6 N ov 2 00 4 q - DEFORMATION OF WITT - BURNSIDE RINGS
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 ring of integers. When q = 1, this coincides with the Witt-Burnside ring introduced by A. To achieve our goal we 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 cas...
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