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Even lattices and certain central extensions of these lattices are used to construct certain algebraic structures in representation theory called vertex operator algebras and their modules. Certain modules are constructed using automorphisms of the chosen lattice. In this project, we explored the lattice structures with certain desirable properties which allow the automorphism to be lifted nicely to an automorphism of the central extension of the lattice. In particular, we generalized certain results of Penn and Sadowski on lattices of type A and D to more general cases, which we call A-like and D-like, and also explored the dependence of the automorphism’s lifting on labeling of the generators of the lattice.
Peleg, Matan, "Automorphisms on Central Extensions of Lattices" (2016). Mathematics Summer Fellows. 5.