Speaker: Serhii Koval, Memorial University/Saint Mary's University
Time/Date: Wednesday, October 14th, 2026, 1 p.m.
Room: HH3017
Title: Generic graded contractions of Lie algebras

Abstract:

Contractions and degenerations of Lie algebras have been extensively studied since the 1950s. The idea is to pass from one Lie algebra to another by some kind of limit process. Another type of contractions was introduced by de Montigny and Patera (1991) in the context of Lie algebras over a field F equipped with a grading by an abelian group G. In this framework, the Lie bracket of two homogeneous elements is modified by a scalar factor that depends on the degrees of the elements. The resulting scaling function must satisfy specific conditions to ensure that the new bracket remains antisymmetric and satisfies Jacobi identity.

We are interested in generic graded contractions, i.e., those that produce a new Lie bracket for any G-graded Lie algebra. They can be viewed as lax monoidal structures on the identity endofunctor of the category of G-graded vector spaces. We show that generic graded contractions with a fixed support S are classified by a certain abelian group H²_S(F^x), which we explicitly describe. We also analyze which generic graded contractions define graded degenerations of a given G-graded Lie algebra.
This talk is based on a joint work with M. Kochetov.
Kochetov M. and Koval S., Generic graded contractions of Lie algebras,  J. Algebra 696 (2026), 245-277. arXiv:2506.00610.

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