NECESSARY CONDITION FOR $IA$-AUTOMORPHISMS IN LEIBNIZ ALGEBRAS

Yıl 2024, Cilt: 7 Sayı: 2, 75 – 84, 31.07.2024

Zeynep Yaptı Özkurt

https://doi.org/10.33773/jum.1428190

Öz

Proje Numarası

FBA-2020-13173

Kaynakça

• 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).
• 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).
• Y. Bahturin, V. Shipilrain, , On Lie Algebras with wild Automorphisms, Results Math., Vol.28, pp.209-213 (1995).
• P.K. Draxl, Skew Fields, London Mathematical Society Lecture Notes Series, Vol.83, Cambridge University Press (1983).
• V. Drensky, A.I. Papıstas, Automorphisms Of Free Left Nilpotent Leibniz Algebras, Communications in Algebra, Vol.33, pp.2957-2975 (2005).
• V. Drensky, G . M. Piacentini Cattaneo, Varieties Of Metabelian Leibniz Algebras, J.Algebra Appl., Vol.1, pp.31-50 (2002).
• J.-L. Loday, T. Pirashvili, Universal Enveloping Algebras of Leibniz algebras and (co)Homology, Math. Ann., Vol.296, pp.139-158 (1993).
• A. A. Mikhalev, U.U. Umirbaev, Subalgebras of free Leibniz algebras, Commun. Algebra Vol.26, pp.435–446 (1998).
• V. Shpilrain, Non-commutative Determinants and Automorphisms of Groups, Comm. Algebra, Vol.25, pp.559-574 (1997).
• 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).
• T. Oki, Computing valuations of the Dieudonn´e determinants, J. Symbolic Comput. Vol.116, pp.284–323 (2023).
• Z. Özkurt, Orbits and test elements in free Leibniz algebras of rank two, Commun. Alg., Vol.43, No.8, pp.3534-3544 (2023).
• Z. Özkurt, Generating sets of F/R′ Leibniz algebras, Georgian Mathematical Journal, Vol.30, No.5, pp.769–773 (2023).
• Z. Özkurt, N.Ekici, An Application of the Dieudonne Determinant: Detecting non-tame Automorphisms, Journal of Lie Theory, Vol.18, pp.205-214 (2008).
• 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).
• T. Ta，S. Adıyaman, Z. Özkurt, , Automorphisms of free metabelian Leibniz algebras, Comm. Algebra, Vol.49, No.10, pp.4348–4359 (2021).

NECESSARY CONDITION FOR $IA$-AUTOMORPHISMS IN LEIBNIZ ALGEBRAS

Yıl 2024, Cilt: 7 Sayı: 2, 75 – 84, 31.07.2024

Zeynep Yaptı Özkurt

https://doi.org/10.33773/jum.1428190

Öz

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.

Anahtar Kelimeler

Leibniz algebra, Automorphisms, Dieudonné Determinant

Destekleyen Kurum

Cukurova University BAP Coordination Council

Proje Numarası

FBA-2020-13173

Kaynakça

• 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).
• 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).
• Y. Bahturin, V. Shipilrain, , On Lie Algebras with wild Automorphisms, Results Math., Vol.28, pp.209-213 (1995).
• P.K. Draxl, Skew Fields, London Mathematical Society Lecture Notes Series, Vol.83, Cambridge University Press (1983).
• V. Drensky, A.I. Papıstas, Automorphisms Of Free Left Nilpotent Leibniz Algebras, Communications in Algebra, Vol.33, pp.2957-2975 (2005).
• V. Drensky, G . M. Piacentini Cattaneo, Varieties Of Metabelian Leibniz Algebras, J.Algebra Appl., Vol.1, pp.31-50 (2002).
• J.-L. Loday, T. Pirashvili, Universal Enveloping Algebras of Leibniz algebras and (co)Homology, Math. Ann., Vol.296, pp.139-158 (1993).
• A. A. Mikhalev, U.U. Umirbaev, Subalgebras of free Leibniz algebras, Commun. Algebra Vol.26, pp.435–446 (1998).
• V. Shpilrain, Non-commutative Determinants and Automorphisms of Groups, Comm. Algebra, Vol.25, pp.559-574 (1997).
• 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).
• T. Oki, Computing valuations of the Dieudonn´e determinants, J. Symbolic Comput. Vol.116, pp.284–323 (2023).
• Z. Özkurt, Orbits and test elements in free Leibniz algebras of rank two, Commun. Alg., Vol.43, No.8, pp.3534-3544 (2023).
• Z. Özkurt, Generating sets of F/R′ Leibniz algebras, Georgian Mathematical Journal, Vol.30, No.5, pp.769–773 (2023).
• Z. Özkurt, N.Ekici, An Application of the Dieudonne Determinant: Detecting non-tame Automorphisms, Journal of Lie Theory, Vol.18, pp.205-214 (2008).
• 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).
• T. Ta，S. Adıyaman, Z. Özkurt, , Automorphisms of free metabelian Leibniz algebras, Comm. Algebra, Vol.49, No.10, pp.4348–4359 (2021).

Toplam 16 adet kaynakça vardır.

Ayrıntılar

Kaynak Göster

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