代数量子群的紧子群与离散子群I
Compact and discrete subgroups of algebraic quantum groups I
摘要：
设$G$是局部紧群.考虑$G$上连续复变函数的C $^*$ -代数$C_0(G)$，在无穷远处趋于0。$G$中的乘积在C $^*$ -代数$C_0(G)$上产生余积$Δ_G$.局部紧{ \it quantum}群是一个C $^*$ -代数$A$和一个在$A$上的余积$Δ$的对$(A,Δ)$，满足一定的条件。这个定义保证了对$(C_0(G),Δ_G)$是局部紧量子群，并且反过来，当底层的C $^*$ -代数$A$是阿贝尔时，每个局部紧量子群$(A,Δ)$都是这种形式。现在假设$G$是具有紧开子群$K$的局部紧群。{ \it多项式类型}的$G$上的复函数代数是具有正积分的稠密乘子霍普夫$^*$ -代数（即代数量子群）。$K$的特征函数是这个代数量子群中的类群投影。本文研究了任意代数量子群中的类群投影。我们发现几个相关的对象，推广的经典对象相关联的一个紧凑的开子群的局部紧群。
英文摘要：
Let $G$ be a locally compact group. Consider the C$^*$-algebra $C_0(G)$ of continuous complex functions on $G$, tending to 0 at infinity. The product in $G$ gives rise to a coproduct $Δ_G$ on the C$^*$-algebra $C_0(G)$. A locally compact {\it quantum} group is a pair $(A,Δ)$ of a C$^*$-algebra $A$ with a coproduct $Δ$ on $A$, satisfying certain conditions. The definition guarantees that the pair $(C_0(G),Δ_G)$ is a locally compact quantum group and that conversely, every locally compact quantum group $(A,Δ)$ is of this form when the underlying C$^*$-algebra $A$ is abelian. Assume now that $G$ is a locally compact group with a compact open subgroup $K$. The algebra of complex functions on $G$ of {\it polynomial type} is a dense multiplier Hopf $^*$-algebra with positive integrals (i.e. an algebraic quantum group}. The characteristic function of $K$ is a group-like projection in this algebraic quantum group. In this paper, we study group-like projections in an arbitrary algebraic quantum group. We find several associated objects that generalize the classical objects associated to a compact open subgroup of a locally compact group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
