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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: On symmetric invariants of Lie algebras

Presented by Oksana Yakimova, Jena

28 September 2015 16:00 in CM221

Let $\mathfrak g$ be a complex reductive Lie algebra. By the Chevalley restriction theorem, the subalgebra of symmetric invariants $S(\mathfrak g)^{\mathfrak g}$ is a polynomial ring in rank $\mathfrak g$ variables. A quest for non-reductive Lie algebras with a similar property has recently become a trend in invariant theory. Several classes have been suggested, centralisers of nilpotent elements (Premet's conjecture), truncated bi-parabolic subalgebras (Joseph's conjecture), $\mathbb Z_2$-contractions (Panyushev's conjecture). We will see that all these conjectures are false and will present some positive examples.

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