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title: "Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory • CBPF Index"
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**Physics Note****Published**

# **Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory**

**Jerzy Lukierski; F. Toppan**

2002

[**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb033/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Generalized%20Space-time%20Supersymmetries%2C%20Division%20Algebras%20and%20Octonionic%20M-theory)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>Jerzy Lukierski; F. Toppan</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>2002</dd>

<dt>Description</dt>
<dd>We describe the set of generalized Poincar\'{e} and conformal superalgebras in $D=4,5$ and $7$ dimensions as two sequences of superalgebraic structures, taking values in the division algebras ${\bf R},{\bf C}$ and ${\bf H}$. The generalized conformal superalgebras are described for $D=4$ by $OSp(1;8|{\bf R})$, for $D=5$ by $SU(4,4;1)$ and for $D=7$ by $U_\alpha U(8;1|{\bf H})$. The relation with other schemes, in particular the framework of conformal spin (super)algebras and Jordan (super)algebras is discussed. By extending the division-algebra-valued superalgebras to octonions we get in $D=11$ an octonionic generalized Poincar\'{e} superalgebra, which we call {\em octonionic M-algebra}, describing the octonionic M-theory. It contains 32 real supercharges but, due to the octonionic structure, only $52$ real bosonic generators remain independent in place of the $528$ bosonic charges of standard $M$-algebra. In octonionic M-theory there is a sort of equivalence between the octonionic M2 (supermembrane) and the octonionic M5 (super-$5$-brane) sectors. We also define the octonionic generalized conformal M-superalgebra, with $239$ bosonic generators.</dd>

<dt>Year</dt>
<dd>2002</dd>

<dt>Number</dt>
<dd>CBPF-NF-001/02</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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