研究了特征为2的代数闭域上广义Witt代数$W(2,\mathbf{1})$的 投射不可分解模, 给出了特征标高度$ht\chi \le 0$的所有投射不可分解模同构类的代表元和Cartan不变量. 并且进一步讨论了既约包络代数$u(W(2,\mathbf{1}),\chi )$ 的表示型.

In this note, all projective indecomposable modules over generalized Witt algebra $W(2,\mathbf{1})$ with character height $\le 0$ in characteristic 2 are realized, and all related Cartan invariants are computed. Furthermore, we discuss the representation type of the reduced enveloping algebra $u(W(2,\mathbf{1}),\chi )$.