Displaying similar documents to “A $\mathbb Z_4^3$-grading on a $56$-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type $E$”

Triple automorphisms of simple Lie algebras

Deng Yin Wang, Xiaoxiang Yu (2011)

Czechoslovak Mathematical Journal

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An invertible linear map ϕ on a Lie algebra L is called a triple automorphism of it if ϕ ( [ x , [ y , z ] ] ) = [ ϕ ( x ) , [ ϕ ( y ) , ϕ ( z ) ] ] for ∀ x , y , z ∈ L . Let 𝔤 be a finite-dimensional simple Lie algebra of rank l defined over an algebraically closed field F of characteristic zero, 𝔭 an arbitrary parabolic subalgebra of 𝔤 . It is shown in this paper that an invertible linear map ϕ on 𝔭 is a triple automorphism if and only if either ϕ itself is an automorphism of 𝔭 or it is the composition of an automorphism of 𝔭 and an extremal map of order 2 . ...

Free associative algebras, noncommutative Gröbner bases, and universal associative envelopes for nonassociative structures

Murray R. Bremner (2014)

Commentationes Mathematicae Universitatis Carolinae

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First, we provide an introduction to the theory and algorithms for noncommutative Gröbner bases for ideals in free associative algebras. Second, we explain how to construct universal associative envelopes for nonassociative structures defined by multilinear operations. Third, we extend the work of Elgendy (2012) for nonassociative structures on the 2-dimensional simple associative triple system to the 4- and 6-dimensional systems.