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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

Generalized omni-Lie algebras

Liangyun CHEN
Chang SUN
Sayfa
409–415
Yayın Tarihi
2022-10-18
DOI
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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

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Amaç & Hipotez:We introduce the notion of generalized omni-Lie algebras from omni-Lie algebras constructed by Weinstein.
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Temel Bulgular & Veri:We introduce the notion of generalized omni-Lie algebras from omni-Lie algebras constructed by Weinstein.
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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:Araştırma Makalesi
📍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.

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Bu Makaleye Atıf Yap

CHEN, L., SUN, C. (2022). Generalized omni-Lie algebras. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 409–415. https://ajindex.com/articles/529633

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Kaynakça (8)

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  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.