CLASSICAL FREENESS OF ORTHOSYMPLECTIC AFFINE VERTEX SUPERALGEBRAS - Creutzig, Thomas; Linshaw, Andrew R.; Song, Bailin (Proceedings of the American Mathematical Society, 2024)
The question of when a vertex algebra is a quantization of the arc space of its associated scheme has recently received a lot of attention in both the mathematics and physics literature. This property was first studied by Tomoyuki Arakawa and Anne Moreau (see their paper in the references), and was given the name “classical freeness” by Jethro van Ekeren and Reimundo Heluani [Comm. Math. Phys. 386 (2021), no. 1, pp. 495-550] in their work on chiral homology. Later, it was extended to vertex superalgebras by Hao Li [Eur. J. Math. 7 (2021), pp. 1689–1728]. In this note, we prove the classical freeness of the simple affine vertex superalgebra Ln(ospm|2r) for all positive integers m, n, r satisfying Formula presented. In particular, it holds for the rational vertex superalgebras Ln(osp1|2r) for all positive integers r, n.
CRIS-Team Scopus Importer:2024-09-20
Keywords: arc space; associated scheme; classical freeness; coset construction; Vertex algebra