$(\epsilon,\delta)$-Freudenthal Kantor triple systems, $\delta$-structurable algebras and Lie superalgebras

• In this paper we discuss $(\epsilon,\delta)$-Freudenthal Kantor triple systems with certain structure on the subspace $L_{-2}$ of the corresponding standard embedding five graded Lie (super)algebra $L(\epsilon,\delta):=L_{-2}\oplus L_{-1}\oplus L_0\oplus L_1\oplus L_2; [L_i,L_j]\subseteq L_{i+j}$. We recall Lie and Jordan structures associated with $(\epsilon,\delta)$-Freudenthal Kantor triple systems (see ref [26],[27]) and we give results for unitary and pseudo-unitary $(\epsilon,\delta)$-Freudenthal Kantor triple systems. Further, we give the notion of $\delta$-structurable algebras and connect them to $(-1,\delta)$-Freudenthal Kantor triple systems and the corresponding Lie (super) algebra construction.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

Lie superalgebras

triple systems

Publication and Content Type

art (subject category)

ref (subject category)