Abstract
The Lie admissible non-associative algebra N A n , m , s ¯ is defined in the papers [Seul Hee Choi, Ki-Bong Nam, Derivations of a restricted Weyl type algebra I, Rocky Mountain J. Math. 37 (6) (2007) 1813–1830; Seul Hee Choi, Ki-Bong Nam, Weyl type non-associative algebra using additive groups I, Algebra Colloq. 14 (3) (2007) 479–488; Ki-Bong Nam, On Some Non-associative Algebras using Additive Groups, Southeast Asian Bull. Math., vol. 27, Springer-Verlag, 2003, 493–500]. We define in this work the algebra N A n i n , m , s ¯ N which generalizes the previous one and is not Lie admissible. We prove that the antisymmetrized Lie algebra ( N A n i n , m , s ¯ N ) - is simple and contains the simple Lie algebra sl m + s ( F ) . We also prove that the matrix ring is embedded in N 0 , n , 0 ¯ .
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