| Title | $(\epsilon,\delta)$-Freudenthal Kantor triple systems, $\delta$-structurable algebras and Lie superalgebras |
| Authors | Noriaki Kamiya, Daniel Mondoc, Susumu Okubo |
| Publication | Algebras, Groups and Geometries |
| Year | 2010 |
| Volume | 2 |
| Issue | 27 |
| Pages | 191 - 206 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Hadronic Press |
| Abstract English | In this paper we discuss $(\epsilon,\delta)$-Freudenthal Kantor triple systems<br> with certain structure on the subspace $L_{-2}$ of the corresponding standard<br> 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)<br> algebra construction. |
| Keywords | Lie superalgebras, triple systems, |
| ISBN/ISSN/Other | ISSN: 0741-9937 |
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