Araştırma Makalesi
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ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS

Yıl 2022, , 61 - 67, 31.07.2022
https://doi.org/10.33773/jum.1141787

Öz

Let $F_m$ be the free metabelian Lie algebra of rank $m$ over a field $K$ of characteristic 0. An automorphism $\varphi$ of $F_m$ is called central if $\varphi$
commutes with every inner automorphism of $F_m$. Such automorphisms form the centralizer $\text{\rm C}(\text{\rm Inn}(F_m))$
of inner automorphism group $\text{\rm Inn}(F_m)$ of $F_m$ in $\text{\rm Aut}(F_m)$. We provide an elementary proof to show that $\text{\rm C}(\text{\rm Inn}(F_m))=\text{\rm Inn}(F_m)$.

Kaynakça

  • Yu.A. Bahturin, Identical Relations in Lie Algebras (Russian), Nauka, Moscow, (1985). Translation: VNU Science Press, Utrecht, (1987).
  • R.M. Bryant, V. Drensky, Dense subgroups of the automorphism groups of free algebras, Canad. J. Math. 45, pp. 1135-1154 (1993).
  • M. J. Curran, D. J. McCaughan, Central automorphisms that are almost inner, Commun. Alg. 29(5), pp. 2081-2087 (2001).
  • G. A. Miller, Dense subgroups of the automorphism groups of free algebras, Mess. of Math. 43, pp. 124 (1913-1914).
  • A.L. Shmel'kin, Wreath products of Lie algebras and their application in the theory of groups (Russian), Trudy Moskov. Mat. Obshch. 29, pp. 247-260 (1973). Translation: Trans. Moscow Math. Soc. 29, pp. 239-252 (1973).
Yıl 2022, , 61 - 67, 31.07.2022
https://doi.org/10.33773/jum.1141787

Öz

Kaynakça

  • Yu.A. Bahturin, Identical Relations in Lie Algebras (Russian), Nauka, Moscow, (1985). Translation: VNU Science Press, Utrecht, (1987).
  • R.M. Bryant, V. Drensky, Dense subgroups of the automorphism groups of free algebras, Canad. J. Math. 45, pp. 1135-1154 (1993).
  • M. J. Curran, D. J. McCaughan, Central automorphisms that are almost inner, Commun. Alg. 29(5), pp. 2081-2087 (2001).
  • G. A. Miller, Dense subgroups of the automorphism groups of free algebras, Mess. of Math. 43, pp. 124 (1913-1914).
  • A.L. Shmel'kin, Wreath products of Lie algebras and their application in the theory of groups (Russian), Trudy Moskov. Mat. Obshch. 29, pp. 247-260 (1973). Translation: Trans. Moscow Math. Soc. 29, pp. 239-252 (1973).
Toplam 5 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Başak Erginkara 0000-0002-3996-2122

Şehmus Fındık 0000-0001-5717-4413

Yayımlanma Tarihi 31 Temmuz 2022
Gönderilme Tarihi 7 Temmuz 2022
Kabul Tarihi 23 Temmuz 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Erginkara, B., & Fındık, Ş. (2022). ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS. Journal of Universal Mathematics, 5(2), 61-67. https://doi.org/10.33773/jum.1141787
AMA Erginkara B, Fındık Ş. ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS. JUM. Temmuz 2022;5(2):61-67. doi:10.33773/jum.1141787
Chicago Erginkara, Başak, ve Şehmus Fındık. “ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS”. Journal of Universal Mathematics 5, sy. 2 (Temmuz 2022): 61-67. https://doi.org/10.33773/jum.1141787.
EndNote Erginkara B, Fındık Ş (01 Temmuz 2022) ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS. Journal of Universal Mathematics 5 2 61–67.
IEEE B. Erginkara ve Ş. Fındık, “ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS”, JUM, c. 5, sy. 2, ss. 61–67, 2022, doi: 10.33773/jum.1141787.
ISNAD Erginkara, Başak - Fındık, Şehmus. “ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS”. Journal of Universal Mathematics 5/2 (Temmuz 2022), 61-67. https://doi.org/10.33773/jum.1141787.
JAMA Erginkara B, Fındık Ş. ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS. JUM. 2022;5:61–67.
MLA Erginkara, Başak ve Şehmus Fındık. “ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS”. Journal of Universal Mathematics, c. 5, sy. 2, 2022, ss. 61-67, doi:10.33773/jum.1141787.
Vancouver Erginkara B, Fındık Ş. ON CENTRAL AUTOMORPHISMS OF FREE METABELIAN LIE ALGEBRAS. JUM. 2022;5(2):61-7.