scholarly journals Split Casimir operator for simple Lie algebras, solutions of Yang–Baxter equations, and Vogel parameters

2021 ◽  
Vol 62 (8) ◽  
pp. 083503
Author(s):  
A. P. Isaev ◽  
S. O. Krivonos
Keyword(s):  
Lie Algebras ◽  
Casimir Operator ◽  
Simple Lie Algebras

scholarly journals Split Casimir Operator and Universal Formulation of the Simple Lie Algebras

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1046
Author(s):  
Alexey Isaev ◽  
Sergey Krivonos
Keyword(s):  
Lie Algebras ◽  
Casimir Operator ◽  
Adjoint Representation ◽  
Simple Lie Algebras ◽  
Casimir Operators ◽  
Explicit Formulae

We construct characteristic identities for the split (polarized) Casimir operators of the simple Lie algebras in adjoint representation. By means of these characteristic identities, for all simple Lie algebras we derive explicit formulae for invariant projectors onto irreducible subrepresentations in T⊗2 in the case when T is the adjoint representation. These projectors and characteristic identities are considered from the viewpoint of the universal description of the simple Lie algebras in terms of the Vogel parameters.

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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