On the geometry of inner ideals

Exceptional Lie Algebras and Related Algebraic and Geometric Structures

“…For 93? as in 5.4 with 3 exceptional simple one obtains the algebra E 8 [18] in a form first introduced by Freudenthal [27]. In fact, as 93?…”

Deformations of 3-algebras

“…5 We will recall this construction here and show how it too gives rise to a metric Leibniz algebra. 4 all the metric 3-Leibniz algebras which have appeared in the construction of three-dimensional superconformal Chern-Simons theories with matter are special cases of a construction due originally to Faulkner.…”

“…5 It follows from the orthogonality and symmetry conditions that ͓x , y , z͔ =−͓y , x , z͔ for all x , y , z W, which is nothing but Eq. 5 It follows from the orthogonality and symmetry conditions that ͓x , y , z͔ =−͓y , x , z͔ for all x , y , z W, which is nothing but Eq.…”

“…12 after an initial attempt by Takhtajan in Ref. 5 We discuss the relevant Leibniz algebra in the general Faulkner construction and set up the deformation theory in the special case of orthogonal representations. Daletskii and Takhtajan in Ref.…”

k-Leibniz algebras from lower order ones: From Lie triple to Lie ℓ-ple systems

“…A class of 3-Leibniz algebras is provided by the Lie triple systems (Sec. 3), introduced in mathematics long ago [25][26][27][28] (see further [29]). They may be defined (Sec.…”