DANIELE BRILLI

PhD Graduate

PhD program:: XXXIII


supervisor: A. De Sole
advisor: A. D'Andrea

Thesis title: Pseudoalgebraic structures and representations of the exceptional Lie superalgebra E(5,10)

The language of Lie pseudoalgebras is useful in giving finite description of infinite-dimensional Lie algebras and has proved to be a valuable tool in algebra and representation theory. In this thesis, we apply pseudoalgebraic techniques to the representation theory of the exceptional linearly compact Lie superalgebra E(5,10). We construct a Lie super pseudoalgebra associated to E(5,10) and use it to find a bound on the degree of singular vectors in generalized Verma modules. We also classify all such pseudoalgebraic structures for E(5,10). We expect that the techniques developed can be suitably generalized.

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