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Ideally constrained Lie algebras

✍ Scribed by Norberto Gavioli; Valerio Monti

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
165 KB
Volume
253
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper we deal with graded Lie algebras L such that there exists a positive integer r such that for every positive integer i and for every homogeneous ideal I L i the inclusion I βŠ‡ L i+r-1 holds. The solvable case and the r = 1 case receive a special attention.

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Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f , d : R β†’ A are linear maps satisfying that f ([x, y]) = f (x)yf (y)x + xd(y)yd(x) for all x, y ∈ R, then there exist a generalized de