What question did this study set out to answer?

To describe the center of semisimple Lie algebras and explore the centers of Lie superalgebras through Lagrangian equivalence relations.

May 16, 2026

Around the center

Key Points

To describe the center of semisimple Lie algebras and explore the centers of Lie superalgebras through Lagrangian equivalence relations.
Introduced Lagrangian equivalence relations to generalize the subgroup action.
Used the algebra of W-invariant functions on the dual of the Cartan subalgebra for analysis.
Presented a new proof without a case-by-case analysis.
Established a new proof of Ian Musson's result on centers of Lie superalgebras.
Demonstrated properties of centers relating to non-finite group actions.
Clarified the connection between Lagrangian equivalence and lie superalgebra centers.

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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Cite This Study

Gorelik et al. (Thu,) studied this question.

synapsesocial.com/papers/6a0809f1a487c87a6a40bd00 https://doi.org/https://doi.org/10.1142/s0218196726410110

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