标题： 接触海藻 显示英文标题

标题： Contact Seaweeds

摘要： 一个 ($2k+1$)$-$维的接触李代数是一个存在一个微分形式$\varphi$的代数，使得$\varphi \wedge (d\varphi)^k\ne0$。 这类代数的指标为一，但这一点通常不是充分条件。 在这里我们证明指标为一的A型海藻代数必定是接触的。 提供了示例以及它们显式构造的方法。 显示英文摘要

摘要： A ($2k+1$)$-$dimensional contact Lie algebra is one which admits a one-form $\varphi$ such that $\varphi \wedge (d\varphi)^k\ne0$. Such algebras have index one, but this is not generally a sufficient condition. Here we show that index-one type-A seaweed algebras are necessarily contact. Examples, together with a method for their explicit construction, are provided.