Mathematical Sciences: Triangular AF Algebras and TriangularHyperfinite Algebras

这个少数民族研究启动奖是为了支持 贝克教授关于非自伴算子代数的研究成果他 对近似的子代数特别感兴趣 有限维C*-代数（分别von Neumann代数 这些因素起着类似于上层建筑的作用 全矩阵代数中的三角矩阵他的问题 将追求主要与分类，同构 不变量和等距与代数同构。 这个项目的核心运营商可能是 被认为是一种丰富的数字。他们遵守相同的 算术定律作为数字，但有两个明显的例外，即 乘法的结果取决于 因子被取，并不是每个非零运算符都有一个 相反。数学分析只知道两个数字系统， 真实的和复杂的，但有一个巨大的各种运算符 代数不适合用数字表示的情况可以 通常用算子代数来表示， 后者具有更大程度的灵活性。 代价是理解了结构， 算子代数的分类需要相当大的努力， 比如这个项目要做的工作。

This Minority Research Initiation award is for the support of Professor Baker's work on nonselfadjoint operator algebras. He is particularly interested in subalgebras of approximately finite-dimensional C*-algebras (resp. von Neumann algebra factors) that play a role analogous to that of the upper triangular matrices in a full matrix algebra. The problems he will pursue have mainly to do with classification, isomorphism invariants, and isometric versus algebraic isomorphism. The operators that lie at the heart of this project may be thought of as a species of enriched numbers. They obey the same laws of arithmetic as numbers with two notable exceptions, namely that the result of multiplication depends on the order in which the factors are taken, and not every nonzero operator has an inverse. Mathematical analysis knows only two number systems, the real and complex, but there is an immense variety of operator algebras. Situations unsuitable for numerical representation can often be represented in some fashion by operator algebras, thanks to the greater degree of flexibility available with the latter. The price for this is that understanding the structure and classification of operator algebras requires considerable effort, as for instance the work to be undertaken in this project.