论文标题
在左侧模块的扩展上，用于meromorthic开弦顶点代数，i
On the extensions of the left modules for a meromorphic open-string vertex algebra, I
论文作者
论文摘要
我们研究了两个左模块的扩展名$ W_1，W_2 $用于Meromorphic开放串线顶点代数$ V $。我们表明，满足某些技术但自然收敛条件的扩展是与与$ v $ -Bimodule $ \ Mathcal {h} _n（W_1，W_2，W_2）$相关的第一个共同体学类别的射击。当$ V $被限制并包含一个不错的顶点subalgebra $ v_0 $时，这些收敛条件会自动保持。此外，我们表明$ \ text {ext}^1的尺寸（w_1，w_2）$在上面的融合规则$ n \ binom {w_2} {w_2} {vw_1} $ in $ v_0 $ -modules的类别中。特别是，如果融合规则是有限的，则$ \ text {ext}^1（w_1，w_2）$为有限维度。我们还举例说明了一个由Virasoro VOA的某些模块组成的Abelian类别，该模块不包含任何不错的亚词法，而收敛条件适用于每个对象。
We study the extensions of two left modules $W_1, W_2$ for a meromorphic open-string vertex algebra $V$. We show that the extensions satisfying some technical but natural convergence conditions are in bijective correspondence to the first cohomology classes associated to the $V$-bimodule $\mathcal{H}_N(W_1, W_2)$ constructed in \cite{HQ-Red}. When $V$ is grading-restricted and contains a nice vertex subalgebra $V_0$, those convergence conditions hold automatically. In addition, we show that the dimension of $\text{Ext}^1(W_1, W_2)$ is bounded above by the fusion rule $N\binom{W_2}{VW_1}$ in the category of $V_0$-modules. In particular, if the fusion rule is finite, then $\text{Ext}^1(W_1, W_2)$ is finite-dimensional. We also give an example of an abelian category consisting of certain modules of the Virasoro VOA that does not contain any nice subalgebras, while the convergence conditions hold for every object.
