Cohomology of the Lie conformal algebra 𝒲(a,b)
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Published:2024-08-03
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Wang Jinrong1ORCID,
Yue Xiaoqing1ORCID
Affiliation:
1. School of Mathematical Sciences, Key Laboratory of Intelligent, Computing and Applications (Ministry of Education), Tongji University, Shanghai 200092, P. R. China
Abstract
The Lie conformal algebra [Formula: see text] with two parameters [Formula: see text] is a free [Formula: see text]-module generated by [Formula: see text] and [Formula: see text] satisfying [Formula: see text] and [Formula: see text], which is the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we determine the basic and reduced cohomology groups of [Formula: see text] for the case of [Formula: see text] with coefficients in its module. In particular, the low-dimensional basic cohomology groups with trivial coefficients are completely determined.
Funder
Fundamental Research Funds for the Central Universities
Publisher
World Scientific Pub Co Pte Ltd