Let $sl_2-mod$ be the category of all finite dimensional $sl_2$-modules and let $U_q(sl_2)-mod$ be the category of all finite dimensional $U_q(sl_2)$-modules, $q$ is not a root of unity. It is said that $sl_2-mod$ is equivalent to $U_q(sl_2)-mod$. What is the functor from $sl_2-mod$ to $U_q(sl_2)-mod$ and what is the functor from $U_q(sl_2)-mod$ to $sl_2-mod$? Thank you very much.
2025-01-13 05:29:02.1736746142
The functor from $sl_2-mod$ to $U_q(sl_2)-mod$.
49 Views Asked by LJR https://math.techqa.club/user/ljr/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 REPRESENTATION-THEORY
- Conjugation preserves representation?
- linear representations, usual assumption
- Example of representation
- Simultaneously diagonalize the regular representation of C2 (+) C2 (+) C2.
- In what sense are the linear characters among the irreducible characters
- representation of sym^2(V)
- Proof that the induced class function $\theta^G$ is a character if $\theta$ is a representation on subgroup
- Character representation of right regular representation as sum of irreducible characters
- For simple $\mathbb C[G]$-modules is the representation unique
- Formulas give irreducible representation, $SL(2, \mathbb{C})$.
Related Questions in QUANTUM-GROUPS
- On proposition I.3.2 of 'Quantum groups' by Kassel.
- Relation between quantum affine algebra $U_q(\widehat{sl_2})$ and the affine Lie algebra $\widehat{sl_2}$?
- Relation between Yangian $Y(sl_2)$ and quantum affine algebra $U_q(\widehat{sl_2})$.
- Graphical calculus for braided Hopf algebras
- Trace of Product of Powers of $A$ and $A^\ast$
- Is the category of all finite dimensional modules of $g$ equivalent to the category of all finite dimensional modules of $U_q(g)$?
- The functor from $sl_2-mod$ to $U_q(sl_2)-mod$.
- Notation in quantum groups.
- GNS construction of a weight
- How to compute Casimir elements of $g \otimes g$?
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