Zhaobing Fan, Jiaqi Huang
We introduce quantum Borcherds-Bozec superalgebras. We present and prove various results of the quantum superalgebras including a bilinear form, higher Serre relation, quasi-R-matrix, character formula for the irreducible highest weight modules. We also prove the category of integrable representations is semi-simple.
Zhaobing Fan, Jiaqi Huang
This paper contains 4 sections, 26 theorems, 170 equations.
Proposition 1.1
There exists a unique bilinear form $(\cdot,\cdot): F \times F \to \mathbb{Q}(q)$ such that $(1,1)=1$ and the following properties hold for all homogeneous elements: The same symbol $(\cdot,\cdot)$ will be used to denote the induced bilinear form on $F \otimes F$, defined by Moreover, the bilinear form on $F$ is symmetric. $\blacktriangleleft$$\blacktriangleleft$
