ScalingStacks

Proposition 3.2.9. $\hat{H}_{n}^{+}$ is a differential graded subalgebra of $\hat{H}_{n}$.

The algebra $\hat{H}_{n}^{+}$ has a presentation with generators $T_{1},\ldots,T_{n-1},c$ and relations

$$T_{i}^{2}=0,\ T_{i}T_{j}=T_{j}T_{i}\text{ if }|i-j|>1,\ T_{i}T_{i+1}T_{i}=T_{i+1}T_{i}T_{i+1}(\text{ if }n>2\ )$$

$$cT_{i}=T_{i+1}c\text{ for }1\leq i<n-1\text{ and }c^{2}T_{n-1}=T_{1}c^{2}.$$