What is the $L$-module structure on $V\otimes W$ where $L$ is a Lie-algebra and $V,W$ are $L$-modules?
The following question is related but I can't find the definition in there: tensor product of modules of Lie algebras
2025-01-12 23:53:41.1736726021
How does a Lie algebra act on a tensor product of L-modules?
520 Views Asked by inclusive https://math.techqa.club/user/inclusive/detail AtRelated Questions in MODULES
- Proper essential extensions
- If module $M = N + mM$, then why is $m(M/N) = M/N$?
- On the invariance of basis number
- Geometric intuition for coherent rings, modules, and sheaves
- Finitely generated iff direct limits of subobjects are bounded by subobjects
- Finding highest weight of a $gl(3)$ submodule of a $gl(4)$-module
- A simple Congruence Equation
- On the $R$-linear independence of free $R$-module
- Do all submodules of $R^n$ have a complement in $R^n$?
- Formulas give irreducible representation, $SL(2, \mathbb{C})$.
Related Questions in LIE-ALGEBRAS
- How do I make sense of terms $X^j\partial_j(Y^i)$ in the Lie bracket of vector fields?
- When derivations are exactly homomorphisms?
- Ideals in Lie algebras
- Lie bracket on $\Gamma(TM\oplus (M\times \mathfrak{g}))$?
- 2-dimensional derived subalgebra of 3-dimensional Lie algebra is abelian
- How are groups with the same Lie Algebra inequivalent?
- Generators of a semi simple lie algebra must be traceless
- From Generators of Lie Groups to Representations
- How does a Lie algebra act on a tensor product of L-modules?
- Representation of a Kac-Moody algebra
Related Questions in TENSOR-PRODUCTS
- Tensor product of two fields
- Coalgebra differential on reduced symmetric algebra
- Double dot product in index notation
- Tensor product isomorphism
- If $\{a_{1},\ldots,a_{n}\}$ is a $K$-basis of $F$, then $\{1\otimes a_{1},\ldots,1\otimes a_{n}\}$ is an $E$-basis of $E\otimes_{K} F$.
- Converting a general tensor element into an elementary tensor
- The $-1$-eigenspace of the exchange map is $V \wedge V$
- Associativity of extension of scalar (tensor product)
- How does a Lie algebra act on a tensor product of L-modules?
- Show that $(2, 0)$ tensor is not a product of two vectors
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity