Triple automorphisms of simple Lie algebras
نویسندگان
چکیده
منابع مشابه
Torsion automorphisms of simple Lie algebras
An automorphism σ of a simple finite dimensional complex Lie algebra g is called torsion, if σ has finite order in the group Aut(g) of all automorphisms of g. The torsion automorphisms of g were classified by Victor Kac in [12], as an application of his results on infinite dimensional Lie algebras. Those torsion automorphisms contained in the identity component G = Aut(g)◦ are called inner; the...
متن کاملAlternating triple systems with simple Lie algebras of derivations
We prove a formula for the multiplicity of the irreducible representation V (n) of sl(2, C) as a direct summand of its own exterior cube ΛV (n). From this we determine that V (n) occurs exactly once as a summand of ΛV (n) if and only if n = 3, 5, 6, 7, 8, 10. These representations admit a unique sl(2)-invariant alternating ternary structure obtained from the projection ΛV (n) → V (n). We calcul...
متن کاملAnosov Automorphisms of Nilpotent Lie Algebras
Each matrix A in GLn(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra fn,r. We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.
متن کاملDomestic Canonical Algebras and Simple Lie Algebras
For each simply-laced Dynkin graph ∆ we realize the simple complex Lie algebra of type ∆ as a quotient algebra of the complex degenerate composition Lie algebra L(A) 1 of a domestic canonical algebra A of type ∆ by some ideal I of L(A) 1 that is defined via the Hall algebra of A, and give an explicit form of I. Moreover, we show that each root space of L(A) 1 /I has a basis given by the coset o...
متن کاملSimple Lie Algebras Which Generalize Witt Algebras
We introduce a new class of simple Lie algebras W (n, m) (see Definition 1) that generalize the Witt algebra by using " exponential " functions, and also a subalgebra W * (n, m) thereof; and we show each derivation of W * (1, 0) can be written as a sum of an inner derivation and a scalar derivation (Theorem. 2) [10]. The Lie algebra W (n, m) is Z-graded and is infinite growth [4].
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2011
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-011-0043-9