# Manchester Algebra Seminar - Philippe Meyer - Dirac operators for colour Lie algebras

Dates: | 2 June 2020 |
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Times: | 14:00 - 15:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, Current University students |

Speaker: Philippe Meyer - University of Oxford

Time: 2pm

Title: Dirac operators for colour Lie algebras.

Abstract: The notion of colour Lie algebra, introduced by Ree (1960), generalises notions of Lie algebra and Lie superalgebra. From an orthogonal representation V of a quadratic colour Lie algebra g, we give a criteria to construct a colour Lie algebra g’ whose bracket extends the bracket of g and the action of g on V. This criteria is used to prove a strange Freudenthal-de Vries formula for basic colour Lie algebras from a Clifford point of view. Following the use of Dirac operators in representation theory initiated by Parthasarathy in 1972, we define cubic Dirac operators for colour Lie algebras and prove a Parthasarathy formula using the same previous criteria.''

Place: Zoom