Year 2020, Volume 49 , Issue 1, Pages 409 - 415 2020-02-06

Generalized omni-Lie algebras

Chang SUN [1] , Liangyun CHEN [2]


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.
omni-Lie algebras, generalized omni-Lie algebras, Dirac structures
  • [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.
Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-1209-895X
Author: Chang SUN
Institution: Northeast Normal University
Country: China


Orcid: 0000-0002-2941-1087
Author: Liangyun CHEN
Institution: Northeast Normal University
Country: China


Dates

Publication Date : February 6, 2020

Bibtex @research article { hujms568290, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {409 - 415}, doi = {10.15672/hujms.568290}, title = {Generalized omni-Lie algebras}, key = {cite}, author = {SUN, Chang and CHEN, Liangyun} }
APA SUN, C , CHEN, L . (2020). Generalized omni-Lie algebras. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 409-415 . DOI: 10.15672/hujms.568290
MLA SUN, C , CHEN, L . "Generalized omni-Lie algebras". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 409-415 <https://dergipark.org.tr/en/pub/hujms/issue/52287/568290>
Chicago SUN, C , CHEN, L . "Generalized omni-Lie algebras". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 409-415
RIS TY - JOUR T1 - Generalized omni-Lie algebras AU - Chang SUN , Liangyun CHEN Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.568290 DO - 10.15672/hujms.568290 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 409 EP - 415 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.568290 UR - https://doi.org/10.15672/hujms.568290 Y2 - 2018 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Generalized omni-Lie algebras %A Chang SUN , Liangyun CHEN %T Generalized omni-Lie algebras %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.568290 %U 10.15672/hujms.568290
ISNAD SUN, Chang , CHEN, Liangyun . "Generalized omni-Lie algebras". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 409-415 . https://doi.org/10.15672/hujms.568290
AMA SUN C , CHEN L . Generalized omni-Lie algebras. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 409-415.
Vancouver SUN C , CHEN L . Generalized omni-Lie algebras. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 415-409.