We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field K. We show that any of such algebras ￡ with a symmetric G-support is of the form ￡ = U-∑jIj with U a subsp...We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field K. We show that any of such algebras ￡ with a symmetric G-support is of the form ￡ = U-∑jIj with U a subspace of ￡1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of ￡, satisfying [Ij, Ik]= 0 if j≠ k. In the case of ￡ being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.展开更多
文摘We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field K. We show that any of such algebras ￡ with a symmetric G-support is of the form ￡ = U-∑jIj with U a subspace of ￡1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of ￡, satisfying [Ij, Ik]= 0 if j≠ k. In the case of ￡ being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.
