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<p>In this work, we introduce the notion of local and 2-local anti-derivations and describe local and 2-local anti-derivations of finite-dimensional solvable Lie algebras with filiform, Heisenberg or abelian nilradicals. We show that any local anti-derivation on the solvable Lie algebras of maximal rank with filiform, Heisenberg or abelian nilradicals, is an anti-derivation. Also, we prove that solvable Lie algebras with filiform nilradical, which have 1-dimension complementary space, admit local anti-derivations which are not anti-derivations. Moreover, similar results concerning 2-local anti-derivations of such algebras are obtained for solvable Lie algebras mentioned above.</p>

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Local and 2-local anti-derivations on solvable Lie algebras

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Shavkat Ayupov,
  • Khusainboy Atajonov,
  • Bakhtiyor Yusupov

摘要

In this work, we introduce the notion of local and 2-local anti-derivations and describe local and 2-local anti-derivations of finite-dimensional solvable Lie algebras with filiform, Heisenberg or abelian nilradicals. We show that any local anti-derivation on the solvable Lie algebras of maximal rank with filiform, Heisenberg or abelian nilradicals, is an anti-derivation. Also, we prove that solvable Lie algebras with filiform nilradical, which have 1-dimension complementary space, admit local anti-derivations which are not anti-derivations. Moreover, similar results concerning 2-local anti-derivations of such algebras are obtained for solvable Lie algebras mentioned above.