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October 8, 2025Open Access

Lie superalgebras in characteristic 2 and mixed characteristic

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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.

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This work introduces lie superalgebras in characteristic 2 and studies their deformation, suggesting new connections in algebraic structures.

Etingof et al. (2025) studied this question.

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This work introduces lie superalgebras in characteristic 2 and studies their deformation, suggesting new connections in algebraic structures.