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arXiv · 2510.03928

Around the center

Maria Gorelik·Vladimir Hinich·Vera Serganova
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Abstract

The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a similar description, but the defining equivalence relation on the dual of the Cartan subalgebra is not given by a finite group action. Lagrangian equivalence relations that we introduce generalize the action of a subgroup of the orthogonal group. Using them, we present a new proof of a result by Ian Musson about the centers of Lie superalgebras. Our proof is not based on a case-by-case analysis.

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Maria Gorelik, Vladimir Hinich, Vera Serganova. 2025-10-04. Around the center. https://arxiv.org/abs/2510.03928

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