论文标题
常规理想，理想的交叉点和商
Regular ideals, ideal intersections, and quotients
论文作者
论文摘要
令$ b \ subseteq a $为c $^*$ - 代数。我们研究了$ b $的常规理想与$ a $的常规理想之间的关系。我们表明，如果$ b \ subseteq a $是常规的c $^*$ - 包容性，并且有一个忠实的有条件期望，从$ a $到$ b $，那么普通的$ a $ a $ a $ a and和by b $不变的常规理想的晶格之间存在同构。我们研究由常规理想保留在商下的包含物的特性。这包括表明，如果$ d \ subseteq a $是cartan包含，而$ j $是$ a $的常规理想，则$ d/d/j \ cap d）$是$ a/j $的cartan subalgebra。我们提供了简化跨产品$ a \rtimes_rγ$的常规理想的描述。
Let $B \subseteq A$ be an inclusion of C$^*$-algebras. We study the relationship between the regular ideals of $B$ and regular ideals of $A$. We show that if $B \subseteq A$ is a regular C$^*$-inclusion and there is a faithful invariant conditional expectation from $A$ onto $B$, then there is an isomorphism between the lattice of regular ideals of $A$ and invariant regular ideals of $B$. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if $D \subseteq A$ is a Cartan inclusion and $J$ is a regular ideal in $A$, then $D/(J\cap D)$ is a Cartan subalgebra of $A/J$. We provide a description of regular ideals in reduced crossed products $A \rtimes_r Γ$.
