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<p>In this paper we introduce the concepts of Lie <i>g</i>-digroups and the affine <i>g</i>-digroup for a Lie <i>g</i>-digroup. Some properties are studied and geometrical aspects of the actions of sub <i>g</i>-digroups of the affine <i>g</i>-digroup are established like in the Lie group case. Moreover, we use infinitesimal action of Lie algebras to determine whether the tangent space to a bar-unit in a <i>g</i>-digroup has a Leibniz algebra structure.</p>

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A preliminary note on Lie g-digroups

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • José Gregorio Rodríguez-Nieto,
  • Olga Patricia Salazar-Díaz,
  • Raúl Velásquez

摘要

In this paper we introduce the concepts of Lie g-digroups and the affine g-digroup for a Lie g-digroup. Some properties are studied and geometrical aspects of the actions of sub g-digroups of the affine g-digroup are established like in the Lie group case. Moreover, we use infinitesimal action of Lie algebras to determine whether the tangent space to a bar-unit in a g-digroup has a Leibniz algebra structure.