U.S.-Brazil Cooperative Research: Operator Algebras

该奖项支持线性代数的合作研究 新墨西哥州大学的特里·洛林和鲁伊 巴西圣保罗大学的埃克塞尔说。 约 有限维（AF）代数是C*-代数， 矩阵代数的归纳极限。 以来 这些矩阵的维数可以任意快速地增长， 归纳系统，许多结果从线性代数是 至少在AF代数的上下文中是没有用的，因为 对维度的依赖性。 这项研究将试图 开发更一般的集合的新不变量， 几乎满足一组关系的矩阵，特别是 不变量，这将对C*-代数的研究产生影响。 此次合作最重要的理由是 是申请人的互补专长。 的 该项目将联合收割机埃克塞尔的专业知识， 决定因素，以及洛林在AF方面的专业知识 代数和算子理论中的相关问题。 他们的 结合专业知识，使他们获得一些有趣的 几乎可交换矩阵的不变量。

This award supports cooperative research on linear algebra between Terry Loring of the University of New Mexico and Ruy Exel of the University of Sao Paulo in Brazil. Approximately finite-dimensional (AF) algebras are C*-algebras which are the inductive limits of algebras of matrices. Since the dimension of these matrices can grow arbitrarily fast in the inductive system, many of the results from linear algebra are not useful, at least in the context of AF algebras, because of the dependence on dimension. This research will attempt to develop new invariants of more general collections of matrices that almost satisfy a set of relations, especially invariants that will have an impact on research in C*-algebras. The most important rationale for this proposed collaboration is the complementary expertise of the applicants. The project will combine Exel's expertise in generalized determinants, and together with Loring's expertise in AF algebras and related issues in operator theory. Their combined expertise has led them to obtain some interesting invariants for the case of almost commuting matrices.