秩为6的非交换实基代数
Noncommutative reality-based algebras of rank 6
摘要：
对具有正度映射的$6$维非交换半单代数的RBA基进行了分类.我们发现，这些RBAs参数化的7个实数，其中前四个是积极的，其余三个任意。我们的分类给出了它们的标准基和结构常数的公式。使用这些，我们给出了一个列表的所有非交换整表代数秩6与秩序高达150。列表中的四个是原始的，但我们表明，这些不能实现为邻接代数的关联计划。在本文的最后一节中，我们应用我们的方法给出了秩为6的两个线性特征标的重数均为1的非交换整表代数的精确描述。
英文摘要：
We classify the RBA-bases of $6$-dimensional noncommutative semisimple algebras for which the algebra has a positive degree map. We show that these RBAs are parametrized by seven real numbers, the first four of which are positive and the remaining three arbitrary. Our classification gives formulas for their standard bases and structure constants. Using these we give a list of all noncommutative integral table algebras of rank 6 with order up to 150. Four in the list are primitive, but we show these cannot be realized as adjacency algebras of association schemes. In the last section of the paper we apply our methods to give a precise description of the noncommutative integral table algebras of rank 6 for which the multiplicity of both linear characters is 1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
