KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 49 Issue: 1

Generalized omni-Lie algebras

Chang Sun(Northeast Normal University)0000-0003-1209-895X
Liangyun Chen(Northeast Normal University)0000-0002-2941-1087
Sayfa
—
Yayın Tarihi
2020-02-06
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We prove that there is a one-to-one correspondence between Dirac structures of a generalized omni-Lie algebra and Lie structures on its linear space.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We introduce the notion of generalized omni-Lie algebras from omni-Lie algebras constructed by Weinstein.
📊
Temel Bulgular & Veri:We introduce the notion of generalized omni-Lie algebras from omni-Lie algebras constructed by Weinstein.
💡
Sonuç & Katkı:We prove that there is a one-to-one correspondence between Dirac structures of a generalized omni-Lie algebra and Lie structures on its linear space.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:omni-Lie algebras · generalized omni-Lie algebras · Dirac structures

Abstract

We introduce the notion of generalized omni-Lie algebras from omni-Lie algebras constructed by Weinstein. We prove that there is a one-to-one correspondence between Dirac structures of a generalized omni-Lie algebra and Lie structures on its linear space.

🔖

Bu Makaleye Atıf Yap

Sun, C., Chen, L. (2020). Generalized omni-Lie algebras. Hacettepe Journal of Mathematics and Statistics, Volume: 49 Issue: 1. https://doi.org/10.15672/hujms.568290

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (8)

  1. Z. Chen and Z. Liu, Omni-Lie algeboids, J. Geom. Phys. 60 (5), 799–808, 2010.
  2. Z. Chen, Z. Liu and Y. Sheng, Dirac structures of omni-Lie algeboids, Int. J. Math. 22 (8), 1163–1185, 2008.
  3. Z. Liu, Some remarks on Dirac structures and Possion reductions, Poisson Geometry Banach Center Publ. 51, 165–173, 2000.
  4. J. Loday, Une version non commutative des alg`ebres de Lie: les alg`ebres de Leibniz, Enseign. Math. 39 (2), 269–293, 1993.
  5. D. Roytenberg and A. Weinstein, Courant algeboids and strongly homotopy Lie algebras, Lett. Math. Phys. 46 (1), 81–93, 1998.
  6. Y. Sheng, Z. Liu and C. Zhu, Omni-Lie 2-algebras and their Dirac structures, J. Geom. Phys. 61 (2), 560–575, 2010.
  7. A. Weinstein, Omni-Lie algebras, RIMS Kokyuroku, 1176, 95–102, 2000.
  8. T. Zhang and Z. Liu, Omni-Lie superalgebras and Lie 2-superalgebras, Front Math. China, 9 (5), 1195–1210, 2014.