On Kähler differentials of divided power algebras

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2023-04-10 DOI:10.1007/s40062-023-00325-2

Ioannis Dokas

引用次数: 0

Abstract

The Quillen–Barr–Beck cohomology of augmented algebras with a system of divided powers is defined as the derived functor of Beck derivations. The main theorem of this paper states that the Kähler differentials of an augmented algebra with a system of divided powers in prime characteristic represents Beck derivations. We give a geometrical interpretation of this statement for the sheaf of relative differentials. As an application in the theory of modular Lie algebras we prove that any special derivation of a divided power algebra is a Beck derivation and we apply the theorem to Witt algebras.

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关于分幂代数的Kähler微分

具有幂分系统的增广代数的Quillen–Barr–Beck上同调被定义为Beck导子的导出函子。本文的主要定理指出，具有素数特征的幂分系统的增广代数的Kähler微分表示Beck导数。我们对相对微分系给出了这一表述的几何解释。作为模李代数理论的一个应用，我们证明了分幂代数的任何特殊导数都是Beck导数，并将该定理应用于Witt代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.