SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

The dimension of products of n homogeneous components in free lie algebras

Nil Mansuroğlu(KIRŞEHİR AHİ EVRAN ÜNİVERSİTESİ)0000-0002-6400-2115
Pages
—
Publication Date
2019-08-01
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

In this paper, we study on products of n homogeneous components in free Lie algebra and we derive formulae for the dimension of such products.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Let L be a free Lie algebra of finite rank r≥2 over a field F and we let L_{m_{i}} denote the degree m_{i} homogeneous component of L.
📊
Key Findings & Data:Ralph Stöhr and Micheal Vaughan-Lee derived formulae for the dimension of the subspaces [L_{m₁},L_{m₂}] for all m₁ and m₂.
💡
Conclusion & Impact:In this paper, we study on products of n homogeneous components in free Lie algebra and we derive formulae for the dimension of such products.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Free Lie algebras · homogeneous component

Abstract

Let L be a free Lie algebra of finite rank r≥2 over a field F and we let L_{m_{i}} denote the degree m_{i} homogeneous component of L. Ralph Stöhr and Micheal Vaughan-Lee derived formulae for the dimension of the subspaces [L_{m₁},L_{m₂}] for all m₁ and m₂. Then, the author and R. Stöhr obtained formulae for the dimension of the products [L_{m₁},L_{m₂},L_{m₃}] under certain conditions on m₁,m₂,m₃. In this paper, we study on products of n homogeneous components in free Lie algebra and we derive formulae for the dimension of such products.

🔖

Cite This Article

Mansuroğlu, N. (2019). The dimension of products of n homogeneous components in free lie algebras. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.457500

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (7)

  1. Magnus W, Karrass A, Solitar D. Combinatorial Group Theory, Presentations of Groups interms of Generators and Relations, New York, NY, USA Dover Publications, 2nd revised ed.,1976.
  2. Mansuroğlu N, Stöhr R. On the dimension of products of homogeneous subspaces in free Liealgebras. Internat. J. Algebra Comput., (2013), 1(23):205-213.
  3. Shirshov A.I. Subalgebras of free Lie algebras. Mat. Sb., (1953), 33:441-452, (in Russian).
  4. Shirshov A.I. Selected works of A. I. Shirshov. Translated from the Russian by Murray Bremnerand Mikhail V. Kotchetov, Edited by Leonid A. Bokut, Victor Latyshev, Ivan Shestakov andEfim Zelmanov, Contemporary Matematicians, Birkhuser Verlag, Basel, viii+242 pp, 2009.
  5. Stöhr R, Vaughan-Lee M. Products of homogeneous subspaces in free Lie algebras, Internat.J. Algebra Comput., (2009), 5(19):699-703.
  6. Witt E. Treue Darstellungen Liescher Ringe. J. Reine Angew. Math., (1937), 177:152-160.
  7. Witt E. Die Unterringe der freien Lieschen Ringe, Math. Z., (1956), 64:195-216.