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May 16, 2026International Journal of Algebra and Computation0 citations

Around the center

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MGM. GorelikVHV. HinichVSV. Serganova

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. (2026) studied this question.

synapsesocial.com/papers/6a0809f1a487c87a6a40bd00https://doi.org/10.1142/s0218196726410110
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