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I study representation theory, cluster algebras, mathematical physics, semigroups.


2d
comment Poisson bivector on the product of two manifolds
@abx, thank you very much. I think that it depends on the Poisson bracket on $C^{\infty}(X \times Y)$. If we define $\{f_1 \otimes g_1, f_2 \otimes g_2\} = \{f_1, f_2\} \otimes g_1g_2 + f_1 f_2 \otimes \{g_1, g_2\}$, then $\pi_{X \times Y} = \pi_X + \pi_Y$. I think that in general, they can be different.
2d
asked Local coordinates on a product of two manifolds.
2d
asked Poisson bivector on the product of two manifolds
Nov
23
comment How to define an action of vector field on $C^{\infty}(M)$?
@John, thank you very much.
Nov
23
asked How to define an action of vector field on $C^{\infty}(M)$?
Nov
23
accepted How to define the vector field $\hat{X}$ on a manifold $M$ defined by an element $X$ in a Lie algebra $\mathfrak{g}$?
Nov
23
asked How to define the vector field $\hat{X}$ on a manifold $M$ defined by an element $X$ in a Lie algebra $\mathfrak{g}$?
Nov
19
accepted How to prove that there is a $\xi$ such that $\frac{f(\xi)}{g(\xi)} = \frac{f''(\xi)}{g''(\xi)}$?
Nov
19
revised How to prove that there is a $\xi$ such that $\frac{f(\xi)}{g(\xi)} = \frac{f''(\xi)}{g''(\xi)}$?
added 75 characters in body
Nov
19
asked How to prove that there is a $\xi$ such that $\frac{f(\xi)}{g(\xi)} = \frac{f''(\xi)}{g''(\xi)}$?
Nov
15
comment What are the elements in $\Gamma(\Lambda^2 TM)$?
thank you very much.
Nov
15
comment What are the elements in $\Gamma(\Lambda^2 TM)$?
thank you very much. I am still confused. I think that $\Pi \in \Gamma(\Lambda^2 TM)$ (not in $\Lambda^2 TM$) and $df \wedge dg \in \Lambda^2 T^*M$ (not in $\Gamma(\Lambda^2 T^*M)$). Why the pairing is between $\Lambda^2 TM$ and $\Lambda^2 T^*M$?
Nov
15
accepted What are the elements in $\Gamma(\Lambda^2 TM)$?
Nov
15
comment What are the elements in $\Gamma(\Lambda^2 TM)$?
if $\beta \in \Gamma(\Lambda^2 T^*M)$, is $\beta$ a map from $M$ to $\Lambda^2 T^*M$? Thank you very much.
Nov
15
comment What are the elements in $\Gamma(\Lambda^2 TM)$?
thank you very much. But usually the value of a pairing $\langle, \rangle$ is in the ground field ( in this case, $\mathbb{R}$ ). But here it seems that we should have the value of $\langle, \rangle$ is in $C^{\infty}(M)$.
Nov
15
revised What are the elements in $\Gamma(\Lambda^2 TM)$?
added 153 characters in body
Nov
15
asked What are the elements in $\Gamma(\Lambda^2 TM)$?
Nov
12
accepted Is supercuspidal representation the same as cuspidal representation?
Nov
4
asked How to show that $U(\mathfrak{n})^* \cong \mathbb{C}[U]$?
Nov
4
comment The Weyl group of $\widehat{\mathfrak{sl}}_2$.
thank you very much.