论文标题
共轭很重要。生物涂抹式Veronese载体和Cayley-Rosenfeld飞机
Conjugation Matters. Bioctonionic Veronese Vectors and Cayley-Rosenfeld Planes
论文作者
论文摘要
我们是由近期代数和几何结构的兴趣促进的，该结构是由分区代数的张量产物及其与高能量理论物理学相关的相关性的，我们分析了通用的生物涂抹式投影和肥大平面。在给出了Veronese表示Cayley Plane $ \ Mathbb {O} p _ {\ Mathbb {C}}}^{2} $的复杂化之后，我们提出了一种新颖的，明确的cayley cayley-cayley-rosenfeld平面$ \ weft（\ mathbb {c} c} c {c} p^{2} $，再次利用Veronese坐标。我们讨论了所有广义生物涂层平面的等轴测组，恢复了特殊组的所有复杂和真实形式$ f_ {4} $和$ e_ {6} $，并表征了对称和遗传性对称空间等平面。我们通过讨论一些可能的物理应用来结束。
Motivated by the recent interest in Lie algebraic and geometric structures arising from tensor products of division algebras and their relevance to high energy theoretical physics, we analyze generalized bioctonionic projective and hyperbolic planes. After giving a Veronese representation of the complexification of the Cayley plane $\mathbb{O}P_{\mathbb{C}}^{2}$, we present a novel, explicit construction of the bioctonionic Cayley-Rosenfeld plane $\left( \mathbb{C}\otimes \mathbb{O}\right) P^{2}$, again by exploiting Veronese coordinates. We discuss the isometry groups of all generalized bioctonionic planes, recovering all complex and real forms of the exceptional groups $F_{4}$ and $E_{6}$, and characterizing such planes as symmetric and Hermitian symmetric spaces. We conclude by discussing some possible physical applications.
