Universal imbedding of a Hom-Lie Triple System

Vandermolen, Robert

doi:10.48550/arxiv.1709.08714

Cited by 1 publication

(4 citation statements)

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“…Although in both cases A 0 is a Lie color algebra, A is not, in general, a (2-graded) Lie color algebra. However, analogously to the paper [41] one can prove that if T is a Hom-Lie triple color system, then A is a Lie color algebra.…”

Section: If Additionally the Identitymentioning

confidence: 74%

“…The standard embedding. This subsection continues the previous one and is inspired by the paper [41]. Here, for T a regular Hom-Leibniz color 3-algebra or a Leibniz color 3-algebra with automorphism we extend the algebra L constructed above by the space isomorphic to T and obtain a larger color (but not necessary color Lie) 2-graded algebra A containing T in a certain sense.…”

Section: If Additionally the Identitymentioning

confidence: 86%

“…Operator algebras. In this subsection, inspired by the ideas of the paper [41], we associate with a Hom-Leibniz color 3-algebra T a certain Lie color algebra L of "derivations" of T, and analogously for a Leibniz color 3-algebra with an automorphism. This construction will be important in the following discussion.…”

Section: If Additionally the Identitymentioning

confidence: 99%

“…Consider then a regular Hom-Leibniz color 3-algebra A Φ . One can then easily see that the subspace T ⊂ A Φ with the induced multiplication, automorphism and G-grading is exactly the algebra (T, [•, •, •], ǫ, φ) (for details, see paper [41]). Definition 2.12.…”

Section: If Additionally the Identitymentioning

confidence: 99%

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Split regular Hom-Leibniz color 3-algebras

Kaygorodov

Popov

2019

Colloq. Math.

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We introduce and describe the class of split regular Hom-Leibniz color 3-algebras as the natural extension of the class of split Lie algebras, split Lie superalgebras, split Lie color algebras, split regular Hom-Lie algebras, split regular Hom-Lie superalgebras, split regular Hom-Lie color algebras, split Leibniz algebras, split Leibniz superalgebras, split Leibniz color algebras, split regular Hom-Leibniz algebras, split regular Hom-Leibniz superalgebras, split regular Hom-Leibniz color algebras, split Lie 3-algebras, split Lie 3-superalgebras, split Lie color 3-algebras, split regular Hom-Lie 3-algebras, split regular Hom-Lie 3superalgebras, split regular Hom-Lie color 3-algebras, split Lie triple systems, split Lie triple supersystems, split Lie triple color systems, split regular Hom-Lie triple systems, split regular Hom-Lie triple supersystems, split regular Hom-Lie triple color systems, split Leibniz 3-algebras, split Leibniz 3-superalgebras, split Leibniz color 3-algebras, split regular Hom-Leibniz 3-algebras, split regular Hom-Leibniz 3-superalgebras, and some other algebras. More precisely, we show that any of such split regular Hom-Leibniz color 3-algebras T is of the form T = U + j I j , with U a subspace of the 0-root space T 0 , and I j an ideal of T satisfying for j = k : [T, I j , I k ] + [I j , T, I k ] + [I j , I k , T ] = 0.Moreover, if T is of maximal length, we characterize the simplicity of T in terms of a connectivity property in its set of non-zero roots.

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Section: If Additionally the Identitymentioning

confidence: 74%

Section: If Additionally the Identitymentioning

confidence: 86%

Section: If Additionally the Identitymentioning

confidence: 99%

Section: If Additionally the Identitymentioning

confidence: 99%

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