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This is a Quantitative Study study.

October 8, 2025Open Access

Lie superalgebras in characteristic 2 and mixed characteristic

Puntos clave

The concept of lie superalgebras over a field in characteristic 2 is established, unifying existing algebra types.
The PBW theorem is proven for the new lie superalgebras, demonstrating their algebraic consistency.
A mixed characteristic deformation theory is developed, enriching the study of these superalgebras.
The study introduces mixed Lie superalgebras over ramified quadratic extensions, linking characteristics 2 and 0.

Resumen

We define the notion of a Lie superalgebra over a field k of characteristic 2 which unifies the two pre-existing ones - Z/2-graded Lie algebras with a squaring map and Lie algebras in the Verlinde category Ver₄^+ (k), and prove the PBW theorem for this notion. We also do the same for the restricted version. Finally, discuss mixed characteristic deformation theory of such Lie superalgebras (for perfect k), introducing and studying a natural lift of our notion of Lie superalgebra to characteristic zero - the notion of a mixed Lie superalgebra over a ramified quadratic extension R of the ring of Witt vectors W (k).

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Cite This Study

Etingof et al. (Wed,) studied this question.

synapsesocial.com/papers/68e6679587ecc93a24d17797 https://doi.org/https://doi.org/10.48550/arxiv.2507.17457

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