AI 中文总结
研究有限维酉群和矩阵代数的迹度量约化积间同态，证明酉群相关稳定性变体等，表明乘积形式同构由特定方式诱导，还得到坐标识别及自同构群的刚性与分类结果，矩阵代数在更一般背景下有类似刚性结果。
AI 中文摘要
我们研究有限维酉群和矩阵代数的迹度量约化积之间的同态，重点是同构。证明了酉群的一种Ulam稳定性变体以及有限维酉群之间几乎满射连续同态的分类，进而表明这些迹约化积的所有乘积形式同构由坐标的几乎置换和自同构的逐坐标应用诱导。我们证明了这些约化积的坐标识别，并在集合论假设下得到其全自同构群的刚性和分类结果。对于迹约化矩阵代数，在保中心*同态的更一般背景下得到了这样的刚性结果。
英文摘要
We study homomorphisms, with a focus on isomorphisms, between the tracial metric reduced products of finite dimensional unitary groups and of matrix algebras. A variant of Ulam stability for unitary groups and a classification of the almost surjective continuous homomorphisms between finite dimensional unitary groups are proved and then used to show that all isomorphisms of product form of these tracial reduced products are induced by almost permutations of the coordinates and coordinatewise application of automorphisms. We prove coordinate recognition for these reduced products and obtain under set theoretic assumptions rigidity and classification results for their full automorphism groups. For tracial reduced matrix algebras we obtain such rigidity result in the more general context of center-preserving $*$-homomorphisms.
Comments27 pages
