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Before I answer your question, let me begin with a brief rant about terminology. The term "lisse" is bad when applied to vertex algebras: It is French for "smooth", but has nothing to do with smooth …

As the link in Erica's comment shows, you can find this in SGA3 Exp. 2, but it is not so easy to extract from the very general language. Here is a rough guide: From Definition 3.9.0, the Lie algebra …

The question of constructing $G$-orbifold vertex algebras amounts to the problem of producing a suitable multiplication operation on a sum of modules for the fixed-point vertex algebra $V^G$. The par …

Given a finite group, the sums of squares of dimensions of irreducible representations add up to the order of the group, so the dimension of an irreducible representation is at most the square root of …

I expect there will never be a classification of simple VOAs, unless perhaps one is only sorting according to very rough criteria. This is because there are too many of them - even the rational case …

Yes. The basic representation of $E_8$ has character $j(\tau)^{1/3} = q^{-1/3}(1+248q+4124q^2 + \cdots)$, and the 4124 decomposes as $1+248+3875$. By Frenkel-Kac-Segal, the basic representation has …

I do not have a complete answer to your questions, but this is what I can say for now: Question 1: A classification is impossible (see the response to question 3). Question 2: Additional examples ar …

The answer to your question is Yes. Consider your covering group $C$ as a central extension: $$1 \to N \to C \to G \to 1$$ and suppose it is given by a 2-cocycle $\alpha \in H^2(G, N)$. Then for any …

A lot has happened in the last four years, and we now have lots of positive results. The current state of knowledge is given in Evans-Gannon, "Reconstruction and Local Extensions for Twisted Group Do …

Suppose I have a prime $p$ and a finite group $G$ together with representations $\sigma: G \to GL_n(\mathbb{Q}_p)$ and $\pi: G \to GL_n(\mathbb{F}_p)$. My question is: When does there exist a rep …

Let $p$ be a prime, let $\mathbb{Z}_p$ be the ring of $p$-adic integers, and let $G$ be a cyclic group of order $p$. It is rather well-known that finite rank $\mathbb{Z}_p$-free representations of $G …

Well, the claim is bogus, so you can't expect the proof to hold much water. On the other hand, it may be instructive to try filling in details to see why it fails. First of all, we can't define conf …

If we just consider central representations, i.e., those for which $z$ acts by a nonzero scalar, then up to a certain kind of equivalence (given by conjugation with algebra isomorphisms) there is a un …

No. Let $G$ be $O_2(\mathbb{R})$, so the Lie algebra is one dimensional, and the center of the universal enveloping algebra is the symmetric algebra of the Lie algebra. Then the usual 2-dimensional …

This is the unique Lemma in section 3.5 of Waterhouse's "Introduction to Affine Group Schemes". It only requires that $G$ be an affine group scheme over a field.