Abstract
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.
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.
Original language | English |
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Pages (from-to) | 191-206 |
Journal | Algebras, Groups and Geometries |
Volume | 2 |
Issue number | 27 |
Publication status | Published - 2010 |
Subject classification (UKÄ)
- Mathematical Sciences
Free keywords
- Lie superalgebras
- triple systems