标题： 群概形及其在对称张量范畴上的李代数 显示英文标题

标题： Group schemes and their Lie algebras over a symmetric tensor category

摘要： 我们研究对称张量范畴上的仿射群概形理论，特别关注在单位处的切空间。 我们证明了该切空间具有受限李代数的结构，可以视为群概形上的一次分布，或者视为坐标环上的右不变导子。 在论文的后半部分，我们在特征为二的对称张量范畴$\mathsf{Ver}_4^+$的具体情况下阐述了这一理论。 显示英文摘要

摘要： We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as the degree one distributions on the group scheme, or as the right invariant derivations on the coordinate ring. In the second half of the paper, we illustrate the theory in the particular case of the symmetric tensor category $\mathsf{Ver}_4^+$ in characteristic two.