Affiliation:
1. Department of mathematics, Faculty of sciences, Arak University, Arak, Iran
Abstract
We study the structure of a graded 3-Lie-Rinehart algebraLover an associative
and commutative graded algebra A. For G an abelian group, we show that if
(L,A) is a tight G-graded 3-Lie-Rinehart algebra, then L and A decompose as
L = ? i?I Li and A = ? j?J Aj, where any Li is a non-zero graded ideal of L
satisfying [Li1 ,Li2 ,Li3] = 0 for any i1, i2, i3 ? I different from each
other, and any Aj is a non-zero graded ideal of A satisfying AjAl = 0 for
any l, j ? J such that j ?l, and both decompositions satisfy that for any i
? I there exists a unique j ? J such that AjLi ? 0. Furthermore, any (Li,Aj)
is a graded 3-Lie-Rinehart algebra. Also, under certain conditions, it is
shown that the above decompositions of L and A are by means of the family of
their, respectively, graded simple ideals.
Publisher
National Library of Serbia
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