增广对合刻板代数范畴中的核与上核
Kernel and cokernel in the category of augmented involutive stereotype algebras
摘要：
我们证明了增广对合刻板代数范畴中的核和上核的几个性质：1）增广对合刻板代数的态射有核和上核，2）上核在到群刻板代数的传递下保持不变，和3）上核的概念允许证明群代数${\mathcal C}^\star(G)$的连续包络$\operatorname{Env} {\mathcal C}^\star(G)$是对合霍普夫代数，原型空间的范畴$({\tt Ste},\odot)$，如果$G$具有形式$Z\cdot K$，其中$Z$是交换局部紧群，$K$是紧群。最后一个结果在推广任意Moore群的Pontryagin对偶中起着重要的作用。
英文摘要：
We prove several properties of kernels and cokernels in the category of augmented involutive stereotype algebras: 1) the morphisms of the augmented involutive stereotype algebras have kernels and cokernels, 2) the cokernel is preserved under the passage to the group stereotype algebras, and 3) the notion of cokernel allows to prove that the continuous envelope $\operatorname{Env} {\mathcal C}^\star(G)$ of the group algebra ${\mathcal C}^\star(G)$ is an involutive Hopf algebra in the category of stereotype spaces $({\tt Ste},\odot)$, if $G$ has the form $Z\cdot K$, where $Z$ is a commutative locally compact group, and $K$ a compact group. The last result plays an important role in the generalization of the Pontryagin duality for arbitrary Moore groups.
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