منابع مشابه
On Lie Algebras of Rank One(')
where h is any additive mapping of G into F (see [1, p. 138]). Each of these algebras is a simple Lie algebra, for which u0 spans a one-dimensional Cartan subalgebra, with one-dimensional root spaces spanned by the ux. We shall prove that under certain hypotheses, these are the only Lie algebras over F of rank one. Kaplansky in [5] has proved that any restricted simple Lie algebra over F of ran...
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It is known that the total (co)-homoloy of a 2-step nilpotent Lie algebra g is at least 2|z|, where z is the center of g. We improve this result by showing that a better lower bound is 2t, where t = |z|+ [ |v|+1 2 ] and v is a complement of z in g. Furthermore, we provide evidence that this is the best possible bound of the form 2t.
متن کاملSpiders for Rank 2 Lie Algebras
A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. It is also known as a spherical category, or a strict, monoidal category with a few extra properties, or by several other names. A recently useful point of view, developed by other authors, of the representation theory of sl(2) has been to present it as a spide...
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A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...
متن کاملCartan Invariants for the Restricted Toral Rank Two Contact Lie Algebra
Restricted modules for the restricted toral rank two contact Lie algebra are considered. Contragredients of the simple modules, Cartan invariants, and dimensions of the simple modules and their projective covers are determined. Let L be a finite dimensional restricted Lie algebra. All L-modules in this paper are assumed to be left, restricted and finite dimensional over the defining field. Each...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90293-1