Characteristically nilpotent extensions of nilradicals of solvable rigid laws



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Ancochea Bermúdez , José María and Campoamor Stursberg, Otto Ruttwig (2001) Characteristically nilpotent extensions of nilradicals of solvable rigid laws. Algebras, Groups and Geometries , 18 (4). pp. 393-399. ISSN 0741-9937

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A Lie algebra g is called characteristically nilpotent if its algebra of derivations is nilpotent. The authors construct the examples of (2m+2)-dimensional characteristically nilpotent Lie algebras g2m+2 with characteristic sequence c(g2m+2) equal to (2m, 1, 1) (c(g) of a nilpotent Lie algebra g is maximum in a lexicographic ordering of the sequence of dimensions of the Jordan blocks of adX, X 2 g−[g, g]). The algebra g2m+2 is obtained by means of three consecutive one-dimensional central extensions e1(L2m−1), e1(e1(L2m−1)), g2m+2 of the filiform Lie algebra L2m−1. L2m−1 is defined by its basis e1, . . . , e2m−1 and commutation relations [e1, ei] = ei+1, 2 i 2m−2.
On the other hand the semi-direct sum t(m,m−1) = Ce1(e1(L2m−1)) of Lie algebras is considered such that t(m,m−1) is a solvable, rigid, complete Lie algebra. Thus the algebra g2m+2 is a one-dimensional central extension of the nilradical of t(m,m−1).

Item Type:Article
Subjects:Sciences > Mathematics > Algebra
ID Code:20939
Deposited On:19 Apr 2013 17:09
Last Modified:12 Dec 2018 15:13

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