I am reading Zhu's famous paper "Modular Invariance and vertex operator algebra". In this paper, Zhu associates each vertex operator algebra with an unital associative algebra, so-called the Zhu's algebra. He proved the one-one correspondence between VOA's module and zhu's algebra's module. I would like to give a simple example for this theorem. I think Heisenberg algebra may be the simplest VOA that I can recall.
2026-03-25 11:03:46.1774436626
What is the Zhu's algebra for Heisenberg VOA
27 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in OPERATOR-ALGEBRAS
- Bijection between $\Delta(A)$ and $\mathrm{Max}(A)$
- hyponormal operators
- Cuntz-Krieger algebra as crossed product
- Identifying $C(X\times X)$ with $C(X)\otimes C(X)$
- If $A\in\mathcal{L}(E)$, why $\lim\limits_{n\to+\infty}\|A^n\|^{1/n}$ always exists?
- Given two projections $p,q$ in a C$^{*}$-algebra $E$, find all irreducible representations of $C^{*}(p,q)$
- projective and Haagerup tensor norms
- AF-algebras and K-theory
- How to show range of a projection is an eigenspace.
- Is $\left\lVert f_U-f_V\right\rVert_{op}\leq \left\lVert U-V\right\rVert_2$ where $f_U = A\mapsto UAU^*$?
Related Questions in CONFORMAL-FIELD-THEORY
- Looking for easy materials on Conformal Field Theory for beginners
- Understanding Moonshine and Heterotic E8xE8
- How the line element change in a complex change of variables?
- Grasping the idea of Virasoro Algebras in 2D Conformal field theory
- Rewriting a state as a field in CFT
- Representations and conformal weights for a Kac Moody algebra
- Unitarity of a representation in the physics literature (in particular in CFT)
- Decomposition of the tensor product of irreducible highet weight infinite dimensional representations (of $Vir$)
- Conformal group in two dimensions
- Different definitions of highest weight representation for affine Lie algebras
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?