JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (4): 56-61.doi: 10.6040/j.issn.1671-9352.0.2024.044

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Derivation extensions and Wells exact sequences of 3-Lie algebras

XU Senrong1, ZHAO Jia2*   

  1. 1. School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, Jiangsu, China;
    2. School of Sciences, Nantong University, Nantong 226019, Jiangsu, China
  • Published:2026-04-08

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Abstract: Given an extension of 3-Lie algebras of the form 0→AiLpB→ 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.

Key words: 3-Lie algebra, extension, derivation, cohomology, Wells exact sequence

CLC Number: 

  • O152
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