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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
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May
22
revised Correspondence between real forms and real structures on complex Lie groups
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May
22
revised Correspondence between real forms and real structures on complex Lie groups
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May
22
revised Correspondence between real forms and real structures on complex Lie groups
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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
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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
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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
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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
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May
4
revised Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
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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.