Mathematical Sciences: K-Theory for Amalgamated Products of C*-Algebras

McClanahan打算继续他对算子代数的k理论的研究，重点是那些作为群的约简C*-代数出现的算子代数。他将利用Lance的六项k群精确序列，得到约简非交换酉群C*-代数和约简非交换格拉斯曼C*-代数的k群。然后，他打算利用皮姆斯纳的技术来推广这一精确序列，使其包括某类C*-代数的满积和约简合并积。这个项目的一般数学领域在希尔伯特空间算子的代数理论中有其基础。运算符可以被认为是有限或无限的复数矩阵。特殊类型的运算符通常放在一个代数中，自然地称为运算符代数。这些看似抽象的对象有着各种各样的应用。例如，它们在结理论中起着关键作用，而结理论目前正被用于研究DNA的结构。

McClanahan intends to continue his study of the K-theory of operator algebras, with emphasis on those that arise as reduced C*- algebras of groups. He will use Lance's six term exact sequence of K-groups to obtain the K-groups of the reduced noncommutative unitary group C*-algebra and the reduced noncommutative Grassmanian C*-algebra. He then intends to use the techniques of Pimsner in order to generalize this exact sequence to include a certain class of full and reduced amalgamated products of C*-algebras. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA.