 Marc Fabbri
Lecturer
Office: Wean Hall 6119
Phone: (412) 268-2557
E-mail: fabbri@andrew.cmu.edu
Research
Lie algebras with Triangular Decomposition include the Kac-Moody, Virasoro and Heisenberg algebras. These admit irreducible representations via Vertex Operators which are important in theoretical physics. Toroidal Lie algebras are generalizations of Kac-Moody algebras, and my work has involved developing representations of a class of Generalized Heisenberg algebras that arise in this setting.
My teaching efforts include developing an approach to calculus which focuses on biological models. I am also interested in the application of elementary group theory to geometry and the history of symmetry and non-Euclidean geometry. Recently I have been working on a classification of plane colored finite symmetry patterns using a method of Coxeter's.
Selected Publications
Fabbri, M.A. & "Coxeter-type classification of coloured finite & symmetry patterns," preprint
Fabbri, M.A. & Okoh, F. "Representations of Virasoro-Heisenberg Algebras and Virasoro-Toroidal algebras", Canad J. Math Vol. 51(3), 1999 523–545.
Fabbri, M.A. & Okoh, F. "Representations of quantum Heisenberg algebras", Can J. Math Vol. 46(5), 1994 pp. 920–929
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