bio | website | mathnet.ru/php/… |
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visits | member for | 3 years, 6 months |
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May 23 |
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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 |
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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 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
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Correspondence between real forms and real structures on complex Lie groups
@YCor: Pardon, I corrected the text in MSE (and here also). |
May 22 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
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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 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
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Correspondence between real forms and real structures on complex Lie groups
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May 22 |
asked | Correspondence between real forms and real structures on complex Lie groups |
May 4 |
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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 |
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Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
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May 4 |
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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 |
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Local coordinates on (infinite dimensional) Lie groups, factorization of Riemann zeta functions
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May 4 |
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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 |
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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 |
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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. |