论文标题
在封闭的谎言理想和广义组代数的中心
On closed Lie ideals and center of generalized group algebras
论文作者
论文摘要
对于任何本地紧凑的集团$ g $和任何Banach代数$ a $，对广义组代数$ l^1（g，a）$的封闭谎言理想的特征是通过$ g $和$ a $获得的。此外，当$ a $是unital的，而$ g $是$ {\ bf [sin]} $ group时，我们表明$ l^1（g，a）$的中心恰恰是所有中心价值功能的收集，这些功能是$ g $的共轭类中不变的。作为一个应用程序，我们确定$ \ MATHCAL {z}（l^1（g）\ otimes^γa）= \ Mathcal {Z}（l^1（g））\ otimes^γ\ Mathcal {z}（z}（z}（a）$，用于一类组和Banach Algebras。而且，在此之前，对于任何有限的组$ g $，组代数$ \ mathbb {c} [g] $的谎言理想是根据$ g $的不可还原字符确定的某些规范空间确定的。
For any locally compact group $G$ and any Banach algebra $A$, a characterization of the closed Lie ideals of the generalized group algebra $L^1(G,A)$ is obtained in terms of left and right actions by $G$ and $A$. In addition, when $A$ is unital and $G$ is an ${\bf [SIN]}$ group, we show that the center of $L^1(G,A)$ is precisely the collection of all center valued functions which are constant on the conjugacy classes of $G$. As an application, we establish that $\mathcal{Z}(L^1(G) \otimes^γ A)= \mathcal{Z}(L^1(G)) \otimes^γ \mathcal{Z}(A)$, for a class of groups and Banach algebras. And, prior to these, for any finite group $G$, the Lie ideals of the group algebra $\mathbb{C}[G]$ are identified in terms of some canonical spaces determined by the irreducible characters of $G$.
