Let $K$ be a field not isomorphic to $\mathbb F_2$, $V = K^n$ - vector space over $K$ on which $\mathrm{GL}(V)$ acts. How to compute cohomology groups $H^i(\mathrm{GL}(V),V)$? It is easy to see that $H^0(\mathrm{GL}(V),V) = 0$ but what about other cohomology groups?
2026-02-22 19:32:06.1771788726
Group cohomology of $\mathrm{GL}(V)$
91 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LINEAR-ALGEBRA
- An underdetermined system derived for rotated coordinate system
- How to prove the following equality with matrix norm?
- Alternate basis for a subspace of $\mathcal P_3(\mathbb R)$?
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Why is necessary ask $F$ to be infinite in order to obtain: $ f(v)=0$ for all $ f\in V^* \implies v=0 $
- I don't understand this $\left(\left[T\right]^B_C\right)^{-1}=\left[T^{-1}\right]^C_B$
- Summation in subsets
- $C=AB-BA$. If $CA=AC$, then $C$ is not invertible.
- Basis of span in $R^4$
- Prove if A is regular skew symmetric, I+A is regular (with obstacles)
Related Questions in HOMOLOGICAL-ALGEBRA
- How does $\operatorname{Ind}^G_H$ behave with respect to $\bigoplus$?
- Describe explicitly a minimal free resolution
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- Tensor product $M\otimes_B Hom_B(M,B)$ equals $End_B(M)$, $M$ finitely generated over $B$ and projective
- Group cohomology of $\mathrm{GL}(V)$
- Existence of adjugant with making given natural transformation be the counit
- Noetherian property is redundant?
- What is the monomorphism that forms the homology group?
- Rational points on conics over fields of dimension 1
- $Ext(-,\mathbb Z)$ for profinite (Galois) groups
Related Questions in GROUP-COHOMOLOGY
- Group cohomology of $\mathrm{GL}(V)$
- How to compute group cohomology $H^2_\sigma(\mathbb{Z}\times \mathbb{Z}, \mathbb{Z}_2\times \mathbb{Z}_2)$ with nontrivial $G$-module
- Group cohomology with the coefficient $\frac{1}{n}\mathbb{Z}/\mathbb{Z}$
- A $G$-module admits a surjection from a $G$-module, which is free as an abelian group, such that the kernel is free
- Different constructions of group homology
- What is the pushout of $D^n \longleftarrow S^{n-1} \longrightarrow D^n$?
- Group theoretic interpretation of the cohomology of $K(G, n)$
- Action of a group on set of morphisms
- Crossed homomorphism/derivation on free group
- Group cohomology: Given $h$ with $dh = 0$ and $[h] = 0 \in H^n(G,A)$, find $f$ s.t. $df = h$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?