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Full-Text Articles in Mathematics
Z2-Orbifolds Of Affine Vertex Algebras And W-Algebras, Masoumah Abdullah Al-Ali
Z2-Orbifolds Of Affine Vertex Algebras And W-Algebras, Masoumah Abdullah Al-Ali
Electronic Theses and Dissertations
Vertex algebras arose in conformal field theory and were first defined axiomatically by Borcherds in his famous proof of the Moonshine Conjecture in 1986. The orbifold construction is a standard way to construct new vertex algebras from old ones. Starting with a vertex algebra V and a group G of automorphisms, one considers the invariant subalgebra VG (called G-orbifold of V), and its extensions. For example, the Moonshine vertex algebra arises as an extension of the Z2-orbifold of the lattice vertex algebra associated to the Leech lattice.
In this thesis we consider two problems. First, …
A Journey To Fuzzy Rings, Brett T. Ernst
A Journey To Fuzzy Rings, Brett T. Ernst
Electronic Theses and Dissertations
Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.