The vertex algebras $$\mathcal {V}^{(p)}$$ and R^{(p)}$$ introduced in Adamovi? (Transform Groups 21(2):299–327, 2016) are very interesting relatives of the well-known triplet logarithmic CFT. algebra (respectively, {R}^{(p)}$$ ) is a large extension simple affine $$L_{k}(\mathfrak {sl}_{2})$$ times Heisenberg algebra), at level $$k=-2+1/p$$ for positive integer p. Particularly, {V}^{(2)}$$ sma...
