Skip to main content
MathOverflow

Return to Question

edited body
Source Link
Rachid
Rachid
  • 121
  • 4

letLet $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ act on $M_{2}(\mathbb{F}_{p})$ by conjugation. My question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?

let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ act on $M_{2}(\mathbb{F}_{p})$ by conjugation. My question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?

Let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ act on $M_{2}(\mathbb{F}_{p})$ by conjugation. My question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?

Fixed minor grammatical issues.
Source Link
Jeremy Rouse
Jeremy Rouse
  • 20.4k
  • 2
  • 79
  • 105

let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ actsact on $M_{2}(\mathbb{F}_{p})$ by conjugation, my. My question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?

let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ acts on $M_{2}(\mathbb{F}_{p})$ by conjugation, my question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?

let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ act on $M_{2}(\mathbb{F}_{p})$ by conjugation. My question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?

Source Link
Rachid
Rachid
  • 121
  • 4

The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$

let $M_{2}(\mathbb{F}_{p})$ be the vector space of 2$\times$2 matrices over the finite field $\mathbb{F}_{p}$ where $p$ is a prime number, and let $GL_{2}(\mathbb{F}_{p})$ be the group of invertible 2$\times$2 matrices over $\mathbb{F}_{p}$. We let $GL_{2}(\mathbb{F}_{p})$ acts on $M_{2}(\mathbb{F}_{p})$ by conjugation, my question is how to compute the cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$ ?