His past research activities have explored: topological Quantum Field Theories in any dimension, BF theories, Cohomology of imbedded loops, Higher dimensional knots; Links, knots and quantum groups; Differential geometrical aspects of string and field theories, Virasoro and Krichever-Novikov algebras; Anomalies in Quantum field theory and their differential geometrical interpretation; and Foundational aspects of Quantum Mechanics.
algebra | Algebra | Lie algebra | linear algebra | Abstract algebra | Linear Algebra | Lie Algebra | Hopf algebra | Clifford algebra | Virasoro algebra | Clifford Algebra | Kac-Moody algebra | Hecke algebra | Filtered algebra | Elementary algebra | Computer algebra system | Boolean algebra | Banach algebra | Affine Lie algebra | abstract algebra | spacetime algebra | Ringel–Hall algebra | ring (algebra) | Regular sequence (algebra) | Poisson algebra | module (algebra) | minor (linear algebra) | Map Algebra | Linear algebra | Jordan frame (Jordan algebra) |
Important examples of vertex operator algebras include lattice VOAs (modeling lattice conformal field theories), VOAs given by representations of affine Kac-Moody algebras (from the WZW model), the Virasoro VOAs (i.e., VOAs corresponding to representations of the Virasoro algebra) and the moonshine module V♮, constructed by Frenkel, Lepowsky and Meurman in 1988.