论文标题
c^* - k组表示的代数
C^*-algebras from k group representations
论文作者
论文摘要
我们介绍了某些$ c^*$ - 代数和$ k $ -graphs与$ k $有限的尺寸统一表示$ρ_1，...，紧凑型组的$ g $的ρ_k$。我们定义了一个较高的等级Doplicher-Roberts代数$ \ Mathcal {O} _ {ρ_1，...，ρ_K} $，由这些表示的张量幂的互动构建。在某些条件下，我们表明，这个$ c^*$ - 代数对$ c^*$ - 行有限等级$ k $ graph $ graph $λ$的$ c^*$的角落是同构的，没有来源。对于$ g $有限的和$ρ_i$忠实的尺寸至少$ 2 $，此图是不可约的，它具有顶点$ \ hat {g} $，边缘由从该组的角色表获得的$ k $通勤矩阵确定。当$ \ Mathcal {o} _ {ρ_1，...，ρ_K} $是简单而纯粹的无限的，以及一些$ k $ - 理论计算时，我们用一些示例说明了一些示例。
We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $ρ_1,...,ρ_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{ρ_1,...,ρ_k}$, constructed from intertwiners of tensor powers of these representations. Under certain conditions, we show that this $C^*$-algebra is isomorphic to a corner in the $C^*$-algebra of a row finite rank $k$ graph $Λ$ with no sources. For $G$ finite and $ρ_i$ faithful of dimension at least $2$, this graph is irreducible, it has vertices $\hat{G}$ and the edges are determined by $k$ commuting matrices obtained from the character table of the group. We illustrate with some examples when $\mathcal{O}_{ρ_1,...,ρ_k}$ is simple and purely infinite, and with some $K$-theory computations.
