Timeline for The action of $GL(\mathbb{R}^{n})\otimes GL(\mathbb{R}^{m})$ on $\mathbb{R}P^{(mn-1)}$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2015 at 16:51 | comment | added | Ali Taghavi | what is the structure of the Lie algebra of this Lie group? | |
| Nov 21, 2015 at 16:03 | vote | accept | Ali Taghavi | ||
| Nov 21, 2015 at 16:02 | comment | added | Mostafa - Free Palestine | @Ali Yes, indeed the closed sets are exactly the orbits of matrices with an upper bound on rank. For the second question, I think $(\mathbb C^*)^n$ action on toric varieties provide a large set of examples. | |
| Nov 21, 2015 at 15:58 | comment | added | Ali Taghavi | Are there some other natural examples that a lie group act on a compact connected manifold but the quotien is a finite non Haussdorfn space? | |
| Nov 21, 2015 at 15:51 | comment | added | Ali Taghavi | because the rank is upper semi continuous? | |
| Nov 21, 2015 at 15:50 | comment | added | Mostafa - Free Palestine | @AliTaghavi Yes, I think it's only determined by rank and so the quotient is a finite set of size $min(m,n)+1$ but its topology is not discrete. | |
| Nov 21, 2015 at 15:43 | comment | added | Ali Taghavi | Thank you for your answer. Does the orbits determined ONLY by rank? If so, is the quotion space a finite discrete space? Is not this strange? | |
| Nov 21, 2015 at 15:32 | history | answered | Mostafa - Free Palestine | CC BY-SA 3.0 |