Biset transformations of Tambara functors
Biset transformations of Tambara functors
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Tambara 函子的 Biset 变换
DOI：
10.1016/j.jalgebra.2013.10.016
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发表时间：
2014
影响因子：
0.9
通讯作者：
Hiroyuki Nakaoka
中科院分区：
文献类型：
--
作者：
Yanagida Shintarou;Yoshioka Kota;Hiroyuki Nakaoka
如果我们对有限群G和H有Anh-G-平分集U，则G上的任何Mackey函子都可以被U变换为Mackey函子ONH。在这篇文章中，我们证明了当U是右自由时，Biset变换也适用于Tambara函子，并且实际上形成了GandH上Tambara函子范畴之间的函子。这种Biset变换函子与Tambara函子上的一些代数运算是相容的，例如理想商或分数。在后半部分中，我们还构造了Biset变换的左伴随。
If we are given anH-G-bisetUfor finite groupsGandH, then any Mackey functor onGcan be transformed byUinto a Mackey functor onH. In this article, we show that the biset transformation is also applicable to Tambara functors whenUis right-free, and in fact forms a functor between the category of Tambara functors onGandH. This biset transformation functor is compatible with some algebraic operations on Tambara functors, such as ideal quotients or fractions. In the latter part, we also construct the left adjoint of the biset transformation.