Generalized weights for operator Lie algebras
نویسندگان
چکیده
منابع مشابه
Lie-type higher derivations on operator algebras
Motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study Lie-type higher derivations on operator algebras in the current work. It is shown that every Lie (triple-)higher derivation on some classical operator algebras is of standard form. The definition of Lie $n$-higher derivations on operator algebras and related pot...
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Proof. I will check the four axioms of the root system. (R1) Since |Φ∨| = |Φ|, then Φ∨ is finite. Since Φ spans E and α∨ is a non-zero scalar multiple of α for all α ∈ Φ, then Φ∨ spans E and 0 / ∈ Φ∨. (R2) Since (−α)∨ = 2(−α) ((−α),(−α)) = − 2α (α,α) = −α∨, then the only multiples of α∨ are ±α∨. (R3) I need to show that if α∨ ∈ Φ∨ then the reflection σα∨ leaves Φ∨ invariant. Let α in Φ, then fo...
متن کاملlie-type higher derivations on operator algebras
motivated by the intensive and powerful works concerning additive mappings of operator algebras, we mainly study lie-type higher derivations on operator algebras in the current work. it is shown that every lie (triple-)higher derivation on some classical operator algebras is of standard form. the definition of lie $n$-higher derivations on operator algebras and related pote...
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In this paper, we introduce a notion of Lie operator algebras which as a generalization of ordinary Lie algebras is an analogy of operator groups. We discuss some elementary properties of Lie operator algebras. Moreover, we also prove a decomposition theorem for Lie operator algebras.
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With the introduction of special roots, we show the existence of some special weights with quite interesting properties for finite Lie algebras. We propose and discuss two statements which lead us to an explicit construction of these special weights and roots. It is seen that the special weights provide us a basis to express Weyl group actions directly no matter what the Weyl group elements wou...
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ژورنال
عنوان ژورنال: Banach Center Publications
سال: 1982
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-8-1-281-287