U.S.-Brazil Cooperative Research: Operator Algebras

该奖项支持新墨西哥大学的Terry looring和巴西圣保罗大学的Ruy Exel在线性代数方面的合作研究。近似有限维代数是C*-代数，它是矩阵代数的归纳极限。由于这些矩阵的维数在归纳系统中可以任意快速增长，因此线性代数的许多结果都是无用的，至少在AF代数的背景下是这样，因为它们依赖于维数。本研究将尝试开发更一般的几乎满足一组关系的矩阵集合的新不变量，特别是将对C*-代数的研究产生影响的不变量。这个提议的合作最重要的理由是申请人的专业知识互补。该项目将结合Exel在广义行列式方面的专业知识，以及Loring在AF代数和算子理论相关问题方面的专业知识。他们的专业知识使他们获得了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.