scholarly journals Tensor products of composition algebras, Albert forms and some exceptional simple Lie algebras

1988 ◽  
Vol 306 (2) ◽  
pp. 667-667 ◽  
Author(s):  
B. N. Allison
Keyword(s):  
Lie Algebras ◽  
Tensor Products ◽  
Simple Lie Algebras ◽  
Composition Algebras

scholarly journals PURELY AFFINE ELEMENTARY su(N) FUSIONS

2002 ◽  
Vol 17 (19) ◽  
pp. 1249-1258 ◽  
Author(s):  
JØRGEN RASMUSSEN ◽  
MARK A. WALTON
Keyword(s):  
Linear Combination ◽  
Lie Algebras ◽  
Tensor Products ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Simple Lie Algebras ◽  
Conformal Field ◽  
Highest Weight ◽  
Highest Weight Representations

We consider three-point couplings in simple Lie algebras — singlets in triple tensor products of their integrable highest weight representations. A coupling can be expressed as a linear combination of products of finitely many elementary couplings. This carries over to affine fusion, the fusion of Wess–Zumino–Witten conformal field theories, where the expressions are in terms of elementary fusions. In the case of su(4) it has been observed that there is a purely affine elementary fusion, i.e. an elementary fusion that is not an elementary coupling. In this paper we show by construction that there is at least one purely affine elementary fusion associated to every su (N > 3).

scholarly journals CODES, S-STRUCTURES, AND EXCEPTIONAL LIE ALGEBRAS

2019 ◽  
Vol 62 (S1) ◽  
pp. S14-S27 ◽  
Author(s):  
ISABEL CUNHA ◽  
ALBERTO ELDUQUE
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Nonassociative Algebras ◽  
Exceptional Lie Algebras

AbstractThe exceptional simple Lie algebras of types E7 and E8 are endowed with optimal $\mathsf{SL}_2^n$ -structures, and are thus described in terms of the corresponding coordinate algebras. These are nonassociative algebras which much resemble the so-called code algebras.

Models of isotropic simple lie algebras

1979 ◽  
Vol 7 (17) ◽  
pp. 1835-1875 ◽  
Author(s):  
B.N. Allison
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras

Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures

2008 ◽  
Author(s):  
P. A. Damianou ◽  
H. Sabourin ◽  
P. Vanhaecke ◽  
Rui Loja Fernandes ◽  
Roger Picken
Keyword(s):  
Lie Algebras ◽  
Poisson Structures ◽  
Nilpotent Orbits ◽  
Simple Lie Algebras

scholarly journals On the construction of simple lie algebras

1973 ◽  
Vol 27 (1) ◽  
pp. 158-183 ◽  
Author(s):  
S Berman
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras
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