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The computer search for finite-dimensional simple Lie algebras over the field \(\mathbb {F}_{2}\) of two elements is discussed. The analytical model of 15-dimensional simple Lie algebras as non-alternating Hamiltonian algebras is constructed. The conjecture that new sporadic simple Lie algebras of dimension 15 obtained by the computer search may be described within the framework of this model.

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New Simple Lie Algebras Found by Computer and Non-alternating Hamiltonian Algebras

  • 会议论文

  • 发表日期：

    2025年

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  • A. V. Kondrateva,
  • M. I. Kuznetsov

摘要

The computer search for finite-dimensional simple Lie algebras over the field \(\mathbb {F}_{2}\) of two elements is discussed. The analytical model of 15-dimensional simple Lie algebras as non-alternating Hamiltonian algebras is constructed. The conjecture that new sporadic simple Lie algebras of dimension 15 obtained by the computer search may be described within the framework of this model.