scholarly journals Nonexistence of standard compact Clifford–Klein forms of homogeneous spaces of exceptional Lie groups

2019 ◽  
Vol 89 (323) ◽  
pp. 1487-1499
Author(s):  
Maciej Bocheński ◽  
Piotr Jastrzȩbski ◽  
Aleksy Tralle
Keyword(s):  
Lie Groups ◽  
Homogeneous Spaces ◽  
Exceptional Lie Groups

scholarly journals Homotopy nilpotency of some homogeneous spaces

2021 ◽  
Author(s):  
Marek Golasiński
Keyword(s):  
Lie Groups ◽  
Homogeneous Spaces ◽  
Complex Numbers ◽  
Grassmann Manifolds ◽  
Loop Spaces ◽  
Exceptional Lie Groups

AbstractLet $${\mathbb {K}}={\mathbb {R}},\,{\mathbb {C}}$$ K = R , C , the field of reals or complex numbers and $${\mathbb {H}}$$ H , the skew $${\mathbb {R}}$$ R -algebra of quaternions. We study the homotopy nilpotency of the loop spaces $$\Omega (G_{n,m}({\mathbb {K}}))$$ Ω ( G n , m ( K ) ) , $$\Omega (F_{n;n_1,\ldots ,n_k}({\mathbb {K}}))$$ Ω ( F n ; n 1 , … , n k ( K ) ) , and $$\Omega (V_{n,m}({\mathbb {K}}))$$ Ω ( V n , m ( K ) ) of Grassmann $$G_{n,m}({\mathbb {K}})$$ G n , m ( K ) , flag $$F_{n;n_1,\ldots ,n_k}({\mathbb {K}})$$ F n ; n 1 , … , n k ( K ) and Stiefel $$V_{n,m}({\mathbb {K}})$$ V n , m ( K ) manifolds. Additionally, homotopy nilpotency classes of p-localized $$\Omega (G^+_{n,m}({\mathbb {K}})_{(p)})$$ Ω ( G n , m + ( K ) ( p ) ) and $$\Omega (V_{n,m}({\mathbb {K}})_{(p)})$$ Ω ( V n , m ( K ) ( p ) ) for certain primes p are estimated, where $$G^+_{n,m}({\mathbb {K}})_{(p)}$$ G n , m + ( K ) ( p ) is the oriented Grassmann manifolds. Further, the homotopy nilpotency classes of loop spaces of localized homogeneous spaces given as quotients of exceptional Lie groups are investigated as well.

scholarly journals Samelson products in p-regular exceptional Lie groups

2014 ◽  
Vol 178 ◽  
pp. 17-29 ◽  
Author(s):  
Sho Hasui ◽  
Daisuke Kishimoto ◽  
Akihiro Ohsita
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups

Geometries of Exceptional Lie Groups. Metasymplectic Geometries

1997 ◽  
pp. 331-369 ◽  
Author(s):  
Boris Rosenfeld
Keyword(s):  
Lie Groups ◽  
Exceptional Lie Groups

scholarly journals The cohomology ring of the spaces of loops on Lie groups and homogeneous spaces

1994 ◽  
Vol 163 (2) ◽  
pp. 361-391 ◽  
Author(s):  
Katsuhiko Kuribayashi
Keyword(s):  
Lie Groups ◽  
Homogeneous Spaces ◽  
Cohomology Ring

scholarly journals Random matrix theory, the exceptional Lie groups andL-functions

2003 ◽  
Vol 36 (12) ◽  
pp. 2933-2944 ◽  
Author(s):  
J P Keating ◽  
N Linden ◽  
Z Rudnick
Keyword(s):  
Lie Groups ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Exceptional Lie Groups
Sign in / Sign up

Export Citation Format

Share Document