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Lie algebras in $\text{Ver}_4^+$
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abstract
We develop Lie theory in the category $\text{Ver}_4^+$ over a field of characteristic 2, the simplest tensor category which is not Frobenius exact, as a continuation of arXiv:2406.10201. We provide a conceptual proof that an operadic Lie algebra in $\text{Ver}_4^+$ is a Lie algebra, i.e. satisfies the PBW theorem, exactly when its invariants form a usual Lie algebra. We then classify low-dimensional Lie algebras in $\text{Ver}_4^+$, construct elements in the center of $U(\mathfrak{gl}(X))$ for $X \in \text{Ver}_4^+$, and study representations of $\mathfrak{gl}(P)$, where $P$ is the indecomposable projective of $\text{Ver}_4^+$.
Forward citations
Cited by 2 Pith papers
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Lie superalgebras in characteristic 2 and mixed characteristic
A unified definition of Lie superalgebras in characteristic 2 is introduced, with PBW theorems and a mixed-characteristic lifting theory.
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Group schemes and their Lie algebras over a symmetric tensor category
Tangent spaces of affine group schemes over symmetric tensor categories are restricted Lie algebras, and the paper computes them explicitly for Ver_4^+ in characteristic 2.
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