3-李代数的导子扩张和Wells正合列

Derivation extensions and Wells exact sequences of 3-Lie algebras

摘要

给定一个3-李代数扩张0→A→ ⁱL→ ^pB→0满足[A,A,L] _L=0,其中i:A→L是包含映射。本文建立3-李代数的1-阶闭链、导子对和2-阶上同调群之间联系的Wells正合列,特别地,当上述扩张可裂时,证明对应的Wells正合列约化为一个短正合列,并且也是可裂的。

Abstract

Given an extension of 3-Lie algebras of the form 0→A→ ⁱL→ ^pB→0 with [A,A,L] _L=0, where i:A→L is the inclusion map. In this paper, we establish the Wells exact sequence which relates 1-order cocycles, derivation pairs and the second cohomology groups of 3-Lie algebras. In particular, when the above extension is split, we show that the corresponding Wells exact sequence is reduced to a short exact sequence and is also split.

关键词

3-李代数 / 扩张 / 导子 / 上同调 / Wells正合列

Key words

3-Lie algebra / extension / derivation / cohomology / Wells exact sequence

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基金资助

国家自然科学基金资助项目(12201253)

江苏省自然科学基金资助项目(BK20220510)