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Octonionic Cayley spinors and $E_{6}$

Tevian Dray, Corinne A. Manogue (2010)

Commentationes Mathematicae Universitatis Carolinae

Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group $E_{6}$ , and of its subgroups. We are therefore led to a description of $E_{6}$ in terms of $3 \times 3$ octonionic matrices, generalizing previous results in the $2 \times 2$ case. Our treatment naturally includes a description of several important subgroups of $E_{6}$ , notably $G_{2}$ , $F_{4}$ , and (the double cover of) $S O (9, 1)$ . An interpretation of the actions...

On a matched pair of Lie groups for the $κ$ -Poincaré in 2-dimensions.

Sitarz, Andrzej, Zgliczyński, Piotr (1996)

Mathematical Physics Electronic Journal [electronic only]

On invariants of continuous subgroups of the generalized Poincaré group $P (1, 4)$ .

Fedorchuk, V. (2002)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

On nets of local algebras on $ℤ^{4}$ , covariant with respect to the discrete Poincaré group ; causality and scattering theory

Hellmut Baumgärtel (1988)

Annales de l'I.H.P. Physique théorique

On parametrization of the linear $GL (4, ℂ)$ and unitary $SU (4)$ groups in terms of Dirac matrices.

Red'kov, Victor M., Bogush, Andrei A., Tokarevskaya, Natalia G. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On some cohomological properties of the Lie algebra of Euclidean motions

Marta Bakšová, Anton Dekrét (2009)

Mathematica Bohemica

The external derivative $d$ on differential manifolds inspires graded operators on complexes of spaces $Λ^{r} g^{*}$ , $Λ^{r} g^{*} \otimes g$ , $Λ^{r} g^{*} \otimes g^{*}$ stated by $g^{*}$ dual to a Lie algebra $g$ . Cohomological properties of these operators are studied in the case of the Lie algebra $g = s e (3)$ of the Lie group of Euclidean motions.

On the contraction of the discrete series of $S U (1, 1)$

C. Cishahayo, S. De Bièvre (1993)

Annales de l'institut Fourier

It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group $𝒫^{1, 1} = S O (1, 1) \otimes_{s} ℝ^{2}$ can be obtained via contraction from the discrete series of representations of $S U (1, 1)$ .

On the uniqueness of the $(2, 2)$ -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.

Peniche, R., Sánchez-Valenzuela, O.A., Thompson, F. (2004)

International Journal of Mathematics and Mathematical Sciences

Displaying 1 – 11 of 11

Octonionic Cayley spinors and $E_{6}$

On a matched pair of Lie groups for the $κ$ -Poincaré in 2-dimensions.

On invariants of continuous subgroups of the generalized Poincaré group $P (1, 4)$ .

On nets of local algebras on $ℤ^{4}$ , covariant with respect to the discrete Poincaré group ; causality and scattering theory

On parametrization of the linear $GL (4, ℂ)$ and unitary $SU (4)$ groups in terms of Dirac matrices.

On some cohomological properties of the Lie algebra of Euclidean motions

On the contraction of the discrete series of $S U (1, 1)$

On the minimal canonical realizations of the Lie algebra $O_{c} (n)$

On the polarizers of compact semi-simple Lie groups. Applications

On the supergroup $S U (m | n)$ and its superfield representations

On the uniqueness of the $(2, 2)$ -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.

Currently displaying 1 – 11 of 11