实李代数的Cayley-Klein格式与Freudhental幻方
"Cayley-Klein" schemes for real Lie algebras and Freudhental Magic Squares
摘要：
我们通过实矩阵、复矩阵或四元数矩阵的实现引入了三个“Cayley-Klein”李代数家族。每个族都包括单实李代数和一些极限拟单实李代数。它们的关系自然导致了一个无限的$3\times 3$ Freudenthal-like幻方家族，它将三个CK家族中的代数联系起来。在最低维的情况下，涉及八元数的适当扩展是可能的，并且对于$N=1, 2$，“经典的”$3\times 3$ Freudenthal-like平方允许$4\times 4$扩展，这给出了原始的Freudenthal平方和Sudbery平方。
英文摘要：
We introduce three "Cayley-Klein" families of Lie algebras through realizations in terms of either real, complex or quaternionic matrices. Each family includes simple as well as some limiting quasi-simple real Lie algebras. Their relationships naturally lead to an infinite family of $3\times 3$ Freudenthal-like magic squares, which relate algebras in the three CK families. In the lowest dimensional cases suitable extensions involving octonions are possible, and for $N=1, 2$, the "classical" $3\times 3$ Freudenthal-like squares admit a $4\times 4$ extension, which gives the original Freudenthal square and the Sudbery square.
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。
