It is still an open problem to determine the conjugacy classes of Borel subalgebras of non-classical type Lie algebras. In this paper, we prove that there are at least 2 conjugacy classes of Borel subalgebras as well as maximal triangulable subalgebras of restricted Cartan type Lie algebras of type W, S and H. We are particularly interested in maximal triangulable subalgebras of $W(n)$ under some conditions which is called $B$-subalgebras (Definition 3.1). We classify the conjugacy classes of $B$-subalgebras for $W(n)$ and determine their representatives.

This paper and its sequel [Z. Lin, K. Ou and B. Shu, Geometric Setting of Jacobson–Witt Algebras, preprint] attempt to establish both algebraic and geometric setting for geometric representation theory of $W(n).$

确定非经典类型李代数的 Borel 子代数的共轭类仍然是一个悬而未决的问题。在本文中，我们证明了至少有 2 个共轭类的 Borel 子代数以及 W、S 和 H 型的限制 Cartan 型李代数的最大可三角子代数。$W(n)$在某些被称为$乙$-次代数（定义 3.1）。我们对共轭类进行分类$乙$- 子代数$W(n)$并确定他们的代表。

本文及其续篇 [Z. Lin, K. Ou 和 B. Shu，Jacobson-Witt 代数的几何设置，预印本] 试图为几何表示理论建立代数和几何设置$W(n).$