In characteristic $0$, what is the Chevalley-Eilenberg (co)homology of a free (graded) Lie algebra? Not the definition, but $H^i =$ ??
2026-02-23 03:00:04.1771815604
What is the (co)homology of a free (graded) Lie algebra?
192 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in HOMOLOGY-COHOMOLOGY
- Are these cycles boundaries?
- Cohomology groups of a torus minus a finite number of disjoint open disks
- $f$ - odd implies $d(f)$ - odd, question to the proof
- Poincarè duals in complex projective space and homotopy
- understanding proof of excision theorem
- proof of excision theorem: commutativity of a diagram
- exact sequence of reduced homology groups
- Doubts about computation of the homology of $\Bbb RP^2$ in Vick's *Homology Theory*
- the quotien space of $ S^1\times S^1$
- Rational points on conics over fields of dimension 1
Related Questions in GRADED-ALGEBRAS
- Direct sum and the inclusion property
- Units are homogeneous in $\mathbb Z$-graded domains
- In a $\mathbb Z$-graded ring we have $IR \cap R_0 = I$
- Is every (left) graded-Noetherian graded ring (left) Noetherian?
- When a homogeneous ideal is written as a product of two ideals, then each of two ideals is homogeneous?
- Tensor product of graded algebras 3
- Trying to understand more about polynomials in noncommuting variables.
- Irreducible highest weight representations as a graded algebra
- Associated Graded Algebra
- The twisted tensor product $BA\otimes_{\tau} A$ as the non-unital Hochschild complex
Related Questions in DIFFERENTIAL-GRADED-ALGEBRAS
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- A condition for a dga to be minimal
- Understanding the algebra structure of $HH(\mathbb{F}_p)$
- DG-Modules over CDG-algebras in the sense of rational homotopy theory.
- quasi isomorphism of two dg algebras
- The twisted tensor product $BA\otimes_{\tau} A$ as the non-unital Hochschild complex
- if $C$ is a filtered coalgebra, does Gr($B\Omega C)\backsimeq B\Omega ($Gr $C)$ hold?
- Categorical product of non-unital associative differential graded coalgebras
- When does a fibration $f:X\rightarrow Y$ in a model category admit a section?.
- Explicit formula for the equalizer of coalgebras
Related Questions in LIE-ALGEBRA-COHOMOLOGY
- Kunneth Formula for Lie Algebra Cohomology
- Virasoro algebra question: Is there a two-surface in Diff($S^1$) with a non-zero integral over the cocycle in $H^2(\mathfrak{g}, \mathbb{C})$?
- Reference Request - Cohomology of the Lie algebra $\mathfrak{u}(n)$ over a finite field?
- duality for (co)homology of Lie algebras
- coboundary operators in relative lie algebra cohomology
- Does the adjoint action induce a trivial action on Lie algebra cohomology?
- By what can we extend a Lie algebra?
- A small sign error?
- Central extension of a Lie algebra, why is the bilinear form a 2-cocycle?
- Difference between Koszul and Chevalley-Eilenberg complexes
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?