Derivations of certain algebras defined by étale descent

Étale Descent of Derivations

We study étale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the multiloop algebras that appear in the construction of extended affine Lie algebras.

Non-commutative integral forms and twisted multi-derivations

Non-commutative connections of the second type or hom-connections and associated integral forms are studied as generalisations of right connections of Manin. First, it is proven that the existence of hom-connections with respect to the universal differential graded algebra is tantamount to the injectivity, and that every finitely cogenerated injective module admits a hom-connection with respect to any differential graded algebra. The bulk of the paper is devoted to describing a method of constructing hom-connections from twisted multi-derivations. The notion of a free twisted multi-derivation …

相邻二次三角导子的不变环

Invariant Rings of Adjacent-Quadratic Triangular Derivations

本文研究特征零域上三角局部幂零导子 $D_5$ 的不变环，证明其为有限生成并给出精确结构，揭示全局下降的两次失败及其机制，并与已知例子比较。