[1] Wang Shengxiang, Wang Shuanhong,. Enveloping algebras of generalized H-Hom-Lie algebras [J]. Journal of Southeast University (English Edition), 2015, 31 (4): 588-590. [doi:10.3969/j.issn.1003-7985.2015.04.027]
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Enveloping algebras of generalized H-Hom-Lie algebras(
)
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 31
- Issue:
- 2015 4
- Page:
- 588-590
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2015-12-30
Info
- Title:
- Enveloping algebras of generalized H-Hom-Lie algebras
- Author(s):
- Wang Shengxiang1; 2; Wang Shuanhong1
-
1Department of Mathematics, Southeast University, Nanjing 211189, China
2School of Mathematics and Statistics, Chuzhou University, Chuzhou 239000, China
- PACS:
- O153.5
- DOI:
- 10.3969/j.issn.1003-7985.2015.04.027
- Abstract:
- Let H be a Hopf algebra and HHHYD the Yetter-Drinfeld category over H. First, the enveloping algebra of generalized H-Hom-Lie algebra L, i.e., Hom-Lie algebra L in the category HHHYD, is constructed. Secondly, it is obtained that U(L)=T(L)/I, where I is the Hom-ideal of T(L)generated by {l⊗l′-l(-1)·l′⊗l0-［l, l′］l, l′∈L}, and u:L→T(L)/I is the canonical map. Finally, as the applications of the result, the enveloping algebras of generalized H-Lie algebras, i.e., the Lie algebras in the category HHHYD and the Hom-Lie algebras in the category of left H-comodules are presented, respectively.
References:
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[12] Wang S H. On the generalized H-Lie structure of associative algebras in Yetter-Drinfeld categories [J]. Comm Algebra, 2002, 30(1): 307-325.
Memo
- Memo:
-
Biographies: Wang Shengxiang(1979—), male, doctor, wangsx-math@163.com; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371088), the Excellent Young Talents Fund of Anhui Province(No.2013SQRL092ZD), the Natural Science Foundation of Higher Education Institutions of Anhui Province(No.KJ2015A294), China Postdoctoral Science Foundation(No.2015M571725), the Excellent Young Talents Fund of Chuzhou University(No.2013RC001).
Citation: Wang Shengxiang, Wang Shuanhong. Enveloping algebras of generalized H-Hom-Lie algebras[J].Journal of Southeast University(English Edition), 2015, 31(4):588-590.[doi:10.3969/j.issn.1003-7985.2015.04.027]