scholarly journals Weight $q$-multiplicities for representations of the exceptional Lie algebra $\mathfrak{g}_2$

2020 ◽  
Vol 27 (5) ◽  
pp. 641-662
Author(s):  
Jerrell Cockerham ◽  
Melissa Gutiérrez González ◽  
Pamela E. Harris ◽  
Marissa Loving ◽  
Amaury V. Miniño ◽  
...  
Keyword(s):  
Lie Algebra ◽  
Exceptional Lie Algebra

scholarly journals Octonions, triality, the exceptional Lie algebra F4 and polar actions on the Cayley hyperbolic plane

2020 ◽  
Vol 31 (07) ◽  
pp. 2050051
Author(s):  
Andreas Kollross
Keyword(s):  
Projective Plane ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Hyperbolic Plane ◽  
Isometry Groups ◽  
Totally Geodesic ◽  
Polar Actions ◽  
Exceptional Lie Algebra ◽  
Explicit Formulae ◽  
Lie Brackets

Using octonions and the triality property of Spin(8), we find explicit formulae for the Lie brackets of the exceptional simple real Lie algebras [Formula: see text] and [Formula: see text], i.e. the Lie algebras of the isometry groups of the Cayley projective plane and the Cayley hyperbolic plane. As an application, we determine all polar actions on the Cayley hyperbolic plane which leave a totally geodesic subspace invariant.

scholarly journals Fibonacci, Golden Ratio, and Vector Bundles

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 426
Author(s):  
Noah Giansiracusa
Keyword(s):  
Lie Algebra ◽  
Moduli Space ◽  
Vector Bundles ◽  
Golden Ratio ◽  
Fibonacci Numbers ◽  
Theoretical Physics ◽  
Stable Curves ◽  
Exceptional Lie Algebra ◽  
Summation Formulas

There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra g2 case of these bundles in three different ways, a family of summation formulas for Fibonacci numbers in terms of the golden ratio is derived.

scholarly journals Basic twist quantization of the exceptional Lie algebra g2

2005 ◽  
Vol 46 (10) ◽  
pp. 103502 ◽  
Author(s):  
Andrzej Borowiec ◽  
Jerzy Lukierski ◽  
Vladimir Lyakhovsky ◽  
Marek Mozrzymas ◽  
Valeriy N. Tolstoy
Keyword(s):  
Lie Algebra ◽  
Exceptional Lie Algebra

scholarly journals Icosahedral Supersymmetry

2014 ◽  
Vol 2 ◽  
pp. 52-54
Author(s):  
J.A. de Wet
Keyword(s):  
Standard Model ◽  
Weyl Group ◽  
Lie Algebra ◽  
Top Quark ◽  
Elementary Particles ◽  
Mckay Correspondence ◽  
Exceptional Lie Algebra ◽  
Icosahedral Group ◽  
Supersymmetric Particles ◽  
The Masses

The Exceptional Lie Algebra E6 used by the Author as a basis forthe Standard Model of the Elementary Particles is a subalgebra of the Lie algebra E8 which in turn is the Lie algebra of the icosahedral group by the McKay correspondence. It is possible to introduce a mass proportional toan entropy given by the the number of permutations of the elements of E6, E8 labeled by the Weyl group W. In this way the masses of the top-quark pair uu and electron are derived without any appeal to QCD and a mass of approximately 19 TeV is predicted for supersymmetric particles.

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