Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$

Details Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$ Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$

2010-12-16

arxiv.org/abs/1012.3514v1

Tsukuba J.Math.27-1(2003),199-215

Mathematics

Differential Geometry

16pages

Scientific paper

For simply connected compact exceptional Lie groups $G = F_4, E_6$ and $E_7$, we consider two involutions $\sigma, \gamma$ and determine the group structure of subgroups $G^{\sigma,\gamma}$ of $G$ which are the intersection $G^\sigma \cap G^{\gamma}$ of the fixed points subgroups of $G^\sigma$ and $G^{\gamma}$. The motivation is as follows. In [1](see the References of this paper), we determine the group structure of $(F_4)^{\sigma, \sigma'}, (E_6)^{\sigma, \sigma'}$ and $(E_7)^{\sigma, \sigma'}$, and in [2](see the References of this paper), we also determine the group structure of $(G_2)^{\gamma, \gamma'}, (F_4)^{\gamma, \gamma'}$ and $(E_6)^{\gamma, \gamma'}$. So, in this paper, we try to determine the type of groups $(F_4)^{\sigma, \gamma}, (E_6)^{\sigma, \gamma}$ and $(E_7)^{\sigma, \gamma}$.

Affiliated with

Also associated with

No associations

Rating

Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fixed points subgroups by two involutive automorphisms $σ, γ$ of compact exceptional Lie groups $F_4, E_6$ and $E_7$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-218470