Spectrum of the Burnside Tambara functor on a cyclic $p$-group

TL;DR

This paper calculates the prime spectrum of the Burnside Tambara functor for cyclic p-groups, advancing the understanding of algebraic structures associated with finite groups in the context of Tambara functors.

Contribution

It provides the first explicit computation of the prime spectrum of the Burnside Tambara functor for cyclic p-groups, extending the algebraic theory of Tambara functors.

Findings

Prime spectrum of the Burnside Tambara functor is explicitly computed for cyclic p-groups.

The work deepens the understanding of the algebraic structure of Tambara functors on finite groups.

Abstract

For a finite group $G$, a Tambara functor on $G$ is regarded as a $G$-bivariant analog of a commutative ring. In this analogy, previously we have defined an ideal of a Tambara functor. In this article, we will demonstrate a calculation of the prime spectrum of the Burnside Tambara functor, when $G$ is a cyclic $p$-group for a prime integer $p$.