Letters in Mathematical Physics

, Volume 70, Issue 2, pp 155–167 | Cite as

Braided m-Lie Algebras

  • Shouchuan Zhang
  • Yao-Zhong Zhang


Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End F M, where M is a Yetter–Drinfeld module over B with dimB < ∞. In particular, generalized classical braided m-Lie algebras slq, f(GM G (A), F) and ospq, t (GM G (A), M, F) of generalized matrix algebra GM G (A) are constructed and their connection with special generalized matrix Lie superalgebra sls, f(GMZ_2(A s ), F) and orthosymplectic generalized matrix Lie super algebra osps, t (GMZ_2(A s ), M s , F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.


lie algebras braided algebras quantum algebras 


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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Shouchuan Zhang
    • 1
    • 2
  • Yao-Zhong Zhang
    • 2
  1. 1.Department of MathematicsHunan UniversityChangshaP.R. China
  2. 2.Department of MathematicsUniversity of QueenslandBrisbaneAustralia

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