Manchester Geometry Seminar - Andrey Lazarev
| Dates: | 12 November 2025 |
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| Times: | 12:00 - 13:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Andrey Lazarev (Lancaster)
Title: Duality for graded Lie algebras (joint work in progress with R. Tang)
Abstract:
Given a finite-dimensional Lie algebra g, its Chevalley-Eilenberg complex CE(g) is an exterior algebra on g and its top exterior power could be a nontrivial cocycle, in which CE(g) has a kind of Poincare duality. This happens when g is unimodular i.e. when the trace of its adjoint representation is zero. If this is not the case, then there is still a twisted version of duality for the cohomology of g, similar to Poincare duality for nonorientable manifolds. These results belong to M. Hazewinkel and are over 50 years old.
What happens when g is graded (or super) Lie algebra? In that case CE(g) is infinite-dimensional, and on the face of it, there is no room for any analogues of the results mentioned above. Nevertheless, there is a framework, based on Koszul duality, which extends duality to the graded context. Unsurprisingly, the notion of the Berezinian is relevant in this context.
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Frank Adams Room 1
Alan Turing Building
Manchester
