Mathematics – Quantum Algebra
Scientific paper
2003-02-03
SIGMA 4 (2008), 057, 35 pages
Mathematics
Quantum Algebra
This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrabilit
Scientific paper
10.3842/SIGMA.2008.057
In this paper we prove that for any commutative (but in general non-associative) algebra $A$ with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra $V = V_0 \oplus V_2 \oplus V_3\oplus ...$, such that $\dim V_0 = 1$ and $V_2$ contains $A$. We can choose $V$ so that if $A$ has a unit $e$, then $2e$ is the Virasoro element of $V$, and if $G$ is a finite group of automorphisms of $A$, then $G$ acts on $V$ as well. In addition, the algebra $V$ can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.
Roitman Michael
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