Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Mathieu-Zhao Subspaces Of Vertex Algebras, Matthew Speck
Mathieu-Zhao Subspaces Of Vertex Algebras, Matthew Speck
Theses and Dissertations
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.