Mathieu-Zhao Subspaces of Vertex Algebras

A Mathieu-Zhao subspace is a generalization of an ideal of an associative ring-algebra, A, first formalized in 2010. A vertex algebra is an algebraic structure first developed in conjunction with string theory in the 1960s and later axiomatized by mathematicians in the 1990s. We formally introduce the definition of a Mathieu-Zhao subspace, M, of a vertex algebra, V. Building on natural connections to associative algebras, we classify an infinite set of non-trivial, non-ideal Mathieu-Zhao subspaces for simple and general vertex algebras by group action eigenspace decomposition. Finally, we state the locally nilpotent epsilon-derivation (LNED) conjecture for vertex algebras