Braided m-Lie Algebras
نویسندگان
چکیده
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 EndFM , where M is a Yetter-Drinfeld module over B with dim B < ∞ . In particular, generalized classical braided m-Lie algebras slq,f (GMG(A), F ) and ospq,t(GMG(A),M,F ) of generalized matrix algebra GMG(A) are constructed and their connection with special generalized matrix Lie superalgebra sls,f (GMZ2(A ), F ) and orthosymplectic generalized matrix Lie super algebra osps,t(GMZ2(A ),M , F ) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.
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