Wiki. “λ-环” [λ-环]

λ-rings are one incarnation of the representation theory of the symmetric groups

λ-rings are all about getting the most for your money when you decategorify a symmetric monoidal abelian category — for example the category of representations of a group, or the category of vector bundles on a topological space.

λ-环到环的遗忘 $$ U \colon \Lambda\mathsf {Ring} \to \mathsf {Ring} $$ 有左右伴随 $\operatorname{Symm}\dashv U\dashv W$, 也即自由和余自由 λ-环.

$\operatorname{Symm}$ 是 “对称函数” 环, 其元素直观上是无穷多变量的无穷多项式, 在变量的任何排列下不变.

例

空间 $X$ 的拓扑 K-理论 $K(X)$ 具有 λ-环结构.