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Cartan matrix
(sometimes called the Cartan integers) where ri are the simple roots of the algebra. The entries are integral from one of the properties of roots. The first condition ...
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Kac–Moody algebra - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Kac%E2%80%93Moody_algebra
The initial construction by Élie Cartan and Wilhelm Killing of finite dimensional simple Lie algebras from the Cartan integers was type dependent. In 1966 ... |
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1, 1975. A NOTE ON THE CARTAN INTEGERS. Morton Curtis and Alan Wiederhold. With each pair of roots of a Lie algebra there is defined a normalized inner ...
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with defect group D. If the Cartan integer cφφ—2 for some φ^IBr(B), there exists a group T which is involved in G and satisfies: T has a normal Sylow p-subgroup ...
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Feb 16, 2010 ... These entries are called “Cartan integers”. The matrix we get, depends on the particular ordering of the base we chose, of course, so the Cartan ...
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The condition αs≠+-αr must be satisfied. CartanInteger(R, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt. The Cartan integer < αr, αsstar > for the root datum R.
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The second inequality is strict because the equality woul correspond to β = ±α. One therefore has that a Cartan integer can only take the values 0, ±1, ±2, ±3.
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the Cartan integers of the simple root system. Throughout this chapter we will be dealing with semi-simple Lie algebras over the complex numbers. 83 ...
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emphasis on the diagnostic test by calculations of Cartan integer characters and involutive bases. Because of the large dimensionality of higher frame bundles, ...
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which we call a Cartan integer. Lemma 1.1. Let (V, Φ) be a root system and let α, β ∈ Φ. Then 〈α, β〉〈β,α〉∈{0, 1, 2, 3}. It follows that the angle between two roots ...
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