论文标题
分级nilpotent Lie组的伪差扩展
Pseudo-differential extension for graded nilpotent Lie groups
论文作者
论文摘要
在$ l^2（g）$上的有限运算符的$^*$ - $^*$ - $^*$ - $^*$ - $^*$ - $ g $ a $ g $ a $ g $上的经典伪分别运算符。我们表明，它的$ c^*$ - 关闭是紧凑型操作员对主要符号的非交换代数的扩展。作为一种新方法，我们使用$ \ mathbb {r} _ {> 0} $的广义固定点代数 - 在$ c^*$ - $ g $的$ c^*$ - 代数中的某个理想中的操作。该动作将$ g $的分级结构计入考虑。我们的构造允许计算符号代数的$ k $理论。
Classical pseudo-differential operators of order zero on a graded nilpotent Lie group $G$ form a $^*$-subalgebra of the bounded operators on $L^2(G)$. We show that its $C^*$-closure is an extension of a noncommutative algebra of principal symbols by compact operators. As a new approach, we use the generalized fixed point algebra of an $\mathbb{R}_{>0}$-action on a certain ideal in the $C^*$-algebra of the tangent groupoid of $G$. The action takes the graded structure of $G$ into account. Our construction allows to compute the $K$-theory of the algebra of symbols.
