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Primitive ideals and derived equivalences for Lie (super) algebras

Kevin Coulembier
(University of Sydney, School of Mathematics and Statistics/Ghent University, Department of Mathematical Analysis)
Kollokvium
Onsdag, 2 december, 2015, at 15:15-16:15, in Aud. D3 (1531-215)
Abstrakt:

We review two recent results in the theory of simple complex Lie algebras and superalgebras; the common denominator being the application of twisting functors.

The first is concerned with the ordering (and classification) of the primitive spectrum for Lie superalgebras. The problem of finding an explicit description was open for over 20 years. We prove that the inclusion order coincides with an analogue of the left Kazhdan-Lusztig order, which can be introduced by a categorical action of the braid group, in terms of twisting.

 The second is the study of derived equivalences between blocks in category O for Lie algebras. Here we obtain an elegant analogue of the classification of ordinary equivalences due to Soergel.
Kontaktperson: Johan P. Hansen