bio | website | mathnet.ru/php/… |
---|---|---|
location | ||
age | ||
visits | member for | 3 years, 10 months |
seen | 2 hours ago | |
stats | profile views | 1,652 |
May
23 |
comment |
Correspondence between real forms and real structures on complex Lie groups
@MikhailBorovoi, excuse me, I did not understand, for which class of groups this is a one-to-one correspondence? And is this a folklore, or there exist references? |
May
22 |
comment |
Correspondence between real forms and real structures on complex Lie groups
@YCor: Yes, I thought the same, an involutive anti-linear Lie algebra automorphism. So this is not a one-to-one correspondence?... I think, at least for reductive groups (i.e. for complexifications of compact real Lie groups) this must be so... That's true? |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 57 characters in body |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 3 characters in body |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 114 characters in body |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
edited body |
May
22 |
comment |
Correspondence between real forms and real structures on complex Lie groups
@YCor: Pardon, I corrected the text in MSE (and here also). |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
added 538 characters in body |
May
22 |
comment |
Correspondence between real forms and real structures on complex Lie groups
Does this give an answer in the case, when $K$ is a compact real Lie group and $G$ is its complexification? |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
edited title |
May
22 |
revised |
Correspondence between real forms and real structures on complex Lie groups
edited title |
May
22 |
asked | Correspondence between real forms and real structures on complex Lie groups |
May
4 |
comment |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Gérard, as far as I understand, the exponential map of $\text{Diff}({\mathbb T})$ is also not locally invertible. I think, you should accept Alexander Schmeding's answer, it sounds much more useful. |
May
4 |
revised |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
added 212 characters in body |
May
4 |
comment |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
@YCor, I thought this means that there is a neighbourhood $U$ of 1 in $G$, and a neighbourhood $V$ of 0 in $L(G)$ such that $\exp(V)=U$. |
May
4 |
revised |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
added 94 characters in body |
May
4 |
revised |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
deleted 2 characters in body |
May
4 |
answered | Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions |
May
4 |
comment |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Gérard, the Lie algebra for ${\mathbb T}^{\mathfrak m}$ is ${\mathbb R}^{\mathfrak m}$, the ${\mathfrak m}$-th power of $\mathbb R$. |
May
4 |
comment |
Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
Gérard, some infinite dimensional locally compact groups have exponential maps that are surjective. For example, the infinite power ${\mathbb T}^{\mathfrak m}$ (where ${\mathfrak m}$ is any infinite cardinal) of the circle $\mathbb T$ has this property. |