Given a vertex operator algebra V, one can construct two associative algebras, the Zhu A(V) and C2-algebra R(V). This gives rise to abelian categories A(V)-Mod R(V)-Mod, in addition category of admissible modules V. In case V is rational C2-cofinite, V-modules all A(V)-modules are equivalent. However, when not rational, connection between these unclear. The goal this paper study triplet W(p), a...

Abstract. There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The ...

Given a complex manifold M endowed with a hermitian metric g and supporting a smooth probability measure μ, there is a naturally associated Dirichlet form operator A on L(μ). If b is a function in L(μ) there is a naturally associated Hankel operator Hb defined in holomorphic function spaces over M . We establish a relation between hypercontractivity properties of the semigroup e−tA and boundedn...

Let LD8(1, 0) and LE8(1, 0) be the simple vertex operator algebras associated to untwisted affine Lie algebra ĝD8 and ĝE8 with level 1 respectively. In the 1980s by I. Frenkel, Lepowsky and Meurman as one of the many important preliminary steps toward their construction of the moonshine module vertex operator algebra, they use roots lattice showing that LD8(1, 0) can embed into LE8(1, 0) as a v...

The Abelian current algebra on the lattice is given from a series of the independent Weyl pairs and the shift operator is constructed by this algebra. So the realization of the operators of the braid group is obtained. For |q| = 1 the shift operator is the product of the theta functions of the generators w n of the current algebra. For |q| = 1 it can be expressed by the quantum dilogarithm of w...

In this article we prove that the full automorphism group of the baby-monster vertex operator superalgebra constructed by Höhn is isomorphic to 2×B, where B is the baby-monster sporadic finite simple group, and determine irreducible modules for the baby-monster vertex operator algebra. Our result has many corollaries. In particular, we can prove that the Z2-orbifold construction with respect to...

Abstract. In this paper, we study certain Virasoro frames for lattice vertex operator algebras and their Z2-orbifolds using linear codes over Z4. We also compute the corresponding frame stabilizer from the view point of binary codes and Z4-codes. As an application, we determine the frame stabilizers of several Virasoro frames of the vertex operator algebra VE8 and the moonshine vertex operator ...

We establish that the Lie algebra of weight one states in a (strongly) rational vertex operator algebra is reductive, and that its Lie rank l is bounded above by the effective central charge c̃. We show that lattice vertex operator algebras may be characterized by the equalities c̃ = l = c, and in particular holomorphic lattice theories may be characterized among all holomorphic vertex operator a...

Let X be a Banach space and T be a bounded linear operator from X to itself (T ∈ B(X).) An operator S ∈ B(X) is a generalized inverse of T if TST = T . In this paper we look at several Banach algebras of operators and characterize when an operator in that algebra has a generalized inverse that is also in the algebra. Also, Drazin inverses will be related to generalized inverses and spectral pro...

We show that the class of unital C-algebras is an elementary class in the language of operator systems. As a result, we have that there is a definable predicate in the language of operator systems that defines the multiplication in any C-algebra. Moreover, we prove that the aforementioned class is ∀∃∀-axiomatizable but not ∀∃-axiomatizable nor ∃∀-axiomatizable. Recall that a C∗-algebra is a ∗-s...