A generalization of the Dress construction for a Tambara functor, and its relation to polynomial Tambara functors

作者：Nakaoka Hiroyuki^*

来源：Advances in Mathematics, 2013, 235: 237-260.

DOI：10.1016/j.aim.2012.11.013

• Tambara functor
• Dress construction
• Mackey functor
• Crossed Burnside ring

For a finite group G, (semi-)Mackey functors and (semi-)Tambara functors are regarded as G-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if G is trivial, they agree with the ordinary (semi-)groups and (semi-)rings, and many naive algebraic properties concerning rings and groups have been extended to these G-bivariant analogous notions. %26lt;br%26gt;In this article, we investigate a G-bivariant analog of the semi-group rings with coefficients. Just as a coefficient ring R and a monoid Q yield the semi-group ring R[Q], our construction enables us to make a Tambara functor T[M] out of a semi-Mackey functor M, and a coefficient Tambara functor T. This construction is a composant of the Tambarization and the Dress construction. %26lt;br%26gt;As expected, this construction is the one uniquely determined by the righteous adjoint property. Besides. in analogy with the trivial group case, if M is a Mackey functor, then T[M] is equipped with a natural Hopf structure. %26lt;br%26gt;Moreover, as an application of the above construction, we also obtain some G-bivariant analogs of the polynomial rings.

• 出版日期2013-3-1