论文标题
简单的lie-kac $ su（2/1）$ Superalgebra及其低水平非对角线超级Casimir操作员
Explicit construction of the finite dimensional indecomposable representations of the simple Lie-Kac $SU(2/1)$ superalgebra and their low level non diagonal super Casimir operators
论文作者
论文摘要
简单的lie-kac超级代数SU（2/1）的所有有限维度不可减少表示形式均以雪佛莉为基础作为复杂矩阵构建。对于典型的表示，杰出的Dynkin标签未量化。然后，我们构建由MARCU，SU和GELMONI归类的通用非典型不可塑性的Quivers以及典型的不可兼容的N基因，用于任何不可减至的模块和任何整数N。奇数发电机中混合订单（2,4）的超级卡西米尔运营商T与超定位分级运算符$χ$成比例，并且满足$ t =χ\; c_2 $，我们定义了一个新的可量化的chiral-casimir $ t^ - = c_2（1-χ2= c_2（1-χ）/2 =（uv+wx）（uv+wx）（vu+x）（vu+xw w where xw where）（vu+xw w where）。在大多数不可分解的情况下，超级症是无角的。我们计算他们的伪元值。
All finite dimensional irreducible representations of the simple Lie-Kac super algebra SU(2/1) are explicitly constructed in the Chevalley basis as complex matrices. For typical representations, the distinguished Dynkin label is not quantized. We then construct the generic atypical indecomposable quivers classified by Marcu, Su and Germoni and typical indecomposable N-generations block triangular extensions for any irreducible module and any integer N. In addition to the quadratic and cubic super-Casimir operators $C_2$ and $C_3$, the supercenter of the enveloping algebra contains a chiral ghost super-Casimir operator T of mixed order (2,4)in the odd generators, proportional to the superidentity grading operator $χ$, and satisfying $T = χ\;C_2$ and we define a new factorizable chiral-Casimir $T^-=C_2(1-χ)/2=(UV+WX)(VU+XW)$ where (U,V,W,X) are the odd generators. In most indecomposable cases, the super-Casimirs are non diagonal. We compute their pseudo-eigenvalues.
