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<p>We study the central extensions of the infinite-dimensional simple <i>n</i>-Lie algebra defined by Filippov, known as the Jacobian algebra. We first show the existence of nontrivial central extensions. Then, we classify all central extensions by computing the second cohomology group.</p>

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Central extensions of n-Lie algebras

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Farukh Mashurov

摘要

We study the central extensions of the infinite-dimensional simple n-Lie algebra defined by Filippov, known as the Jacobian algebra. We first show the existence of nontrivial central extensions. Then, we classify all central extensions by computing the second cohomology group.