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Journals / Journal of Universal Mathematics / 2026 / Cilt: 7 Sayı: 2

NECESSARY CONDITION FOR $IA$-AUTOMORPHISMS IN LEIBNIZ ALGEBRAS

Zeynep Yaptı Özkurt(ÇUKUROVA ÜNİVERSİTESİ)0000-0001-9703-3463
Pages
75–84
Publication Date
2024-07-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

This method is explicitly based on Dieudonn\'{e} determinant.

📌 3 Key Takeaways

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Objective & Hypothesis:Let $F$ be the free Leibniz algebra generated by the set $% X=\{x_{1},...,x_{n}\}$ over the field $K$ of characteristic $0$. consider $R$ as an ideal of $F$.
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Key Findings & Data:This study initially derives an explicit matrix representation for the $IA$-automorphisms of the Leibniz algebra $F/R^{\prime }$.
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Conclusion & Impact:This method is explicitly based on Dieudonn\'{e} determinant.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Leibniz algebra · Automorphisms · Dieudonné Determinant

Abstract

Let $F$ be the free Leibniz algebra generated by the set $% X=\{x_{1},...,x_{n}\}$ over the field $K$ of characteristic $0$. consider $R$ as an ideal of $F$. This study initially derives an explicit matrix representation for the $IA$-automorphisms of the Leibniz algebra $F/R^{\prime }$. Subsequently, we establish a necessary condition for an $IA$% -endomorphism of $F/R^{\prime }$ to be an $IA$-automorphism. This method is explicitly based on Dieudonn\'{e} determinant.

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Cite This Article

Özkurt, Z. Y. (2024). NECESSARY CONDITION FOR $IA$-AUTOMORPHISMS IN LEIBNIZ ALGEBRAS. Journal of Universal Mathematics, Cilt: 7 Sayı: 2, 75–84. https://doi.org/10.33773/jum.1428190

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References (19)

  1. A. T. Abdykhalykov, A. A. Mikhalev, U. U. Umirbaev, Automorphism of two-generated free Leibniz algebras. Commun. Algebra, Vol.29, No.7, pp.2953–2960 (2001).
  2. Y. Bahturin, S. Nabiyev, 9Automorphisms and Derivations of Abelian Extensions of Some Lie Algebras, Abh. Math. Sem. Univ. Hamburg, Vol.62, pp.43-57 (1992).
  3. Y. Bahturin, V. Shipilrain,, On Lie Algebras with wild Automorphisms, Results Math., Vol.28, pp.209-213 (1995).
  4. P.K. Draxl, Skew Fields, London Mathematical Society Lecture Notes Series, Vol.83, Cambridge University Press (1983).
  5. V. Drensky, A.I. Papıstas, Automorphisms Of Free Left Nilpotent Leibniz Algebras, Communications in Algebra, Vol.33, pp.2957-2975 (2005).
  6. V. Drensky, G. M. Piacentini Cattaneo, Varieties Of Metabelian Leibniz Algebras, J.Algebra Appl., Vol.1, pp.31-50 (2002).
  7. J.-L. Loday, T. Pirashvili, Universal Enveloping Algebras of Leibniz algebras and (co)Homology, Math. Ann., Vol.296, pp.139-158 (1993).
  8. A. A. Mikhalev, U.U. Umirbaev, Subalgebras of free Leibniz algebras, Commun. Algebra Vol.26, pp.435–446 (1998).
  9. V. Shpilrain, Non-commutative Determinants and Automorphisms of Groups, Comm. Algebra, Vol.25, pp.559-574 (1997).
  10. A.L. Smel’kin, Wreath products of Lie Algebras and Their Application in the Theory of Groups, Trans. Mosc. Math. Soc., Vol.29, pp.247-260 (1973).
  11. T. Oki, Computing valuations of the Dieudonn´e determinants, J. Symbolic Comput. Vol.116, pp.284–323 (2023).
  12. Z. Özkurt, Orbits and test elements in free Leibniz algebras of rank two, Commun. Alg., Vol.43, No.8, pp.3534-3544 (2023).
  13. Z. Özkurt, Generating sets of F/R′ Leibniz algebras, Georgian Mathematical Journal, Vol.30, No.5, pp.769–773 (2023).
  14. Z. Özkurt, N.Ekici, An Application of the Dieudonne Determinant: Detecting non-tame Automorphisms, Journal of Lie Theory, Vol.18, pp.205-214 (2008).
  15. T. Ta，S. Adıyaman, Z. Özkurt, Automorphisms of free metabelian Leibniz algebras of rank three, Turkish J. Math., Vol.43, No. 5, pp.2262–2274 (2019).
  16. T. Ta，S. Adıyaman, Z. Özkurt,, Automorphisms of free metabelian Leibniz algebras, Comm. Algebra, Vol.49, No.10, pp.4348–4359 (2021).
  17. Y. Bahturin, V. Shipilrain,, On Lie Algebras with wild Automorphisms, Results Math., Vol.28, pp.209-213 (1995).
  18. V. Drensky, G. M. Piacentini Cattaneo, Varieties Of Metabelian Leibniz Algebras, J.Algebra Appl., Vol.1, pp.31-50 (2002).
  19. T. Ta，S. Adıyaman, Z. Özkurt,, Automorphisms of free metabelian Leibniz algebras, Comm. Algebra, Vol.49, No.10, pp.4348–4359 (2021).