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[1] Zhu Haixing, Liu Guohua,. On braided Lie algebras [J]. Journal of Southeast University (English Edition), 2011, 27 (2): 227-229. [doi:10.3969/j.issn.1003-7985.2011.02.024]
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On braided Lie algebras()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
27
Issue:
2011 2
Page:
227-229
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2011-06-30

Info

Title:
On braided Lie algebras
Author(s):
Zhu Haixing;  Liu Guohua
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
Hopf algebra;  braided monoidal category;  braided Lie algebra
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2011.02.024
Abstract:
Let(C, C)be a braided monoidal category. The relationship between the braided Lie algebra and the left Jacobi braided Lie algebra in the category(C, C)is investigated. First, a braided C2-commutative algebra in the category(C, C)is defined and three equations on the braiding in the category(C, C)are proved. Secondly, it is verified that(A, [, ])is a left(strict)Jacobi braided Lie algebra if and only if(A, [, ])is a braided Lie algebra, where A is an associative algebra in the category(C, C). Finally, as an application, the structures of braided Lie algebras are given in the category of Yetter-Drinfel’d modules and the category of Hopf bimodules.

References:

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Memo

Memo:
Biographies: Zhu Haixing(1979—), male, graduate; Liu Guohua(corresponding author), female, doctor, lecturer, liuguohua2000cn@yahoo.com.cn.
Foundation item: The National Natural Science Foundation of China(No.10871042).
Citation: Zhu Haixing, Liu Guohua.On braided Lie algebras[J].Journal of Southeast University(English Edition), 2011, 27(2):227-229.[doi:10.3969/j.issn.1003-7985.2011.02.024]
Last Update: 2011-06-20