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Register a new userA root space decomposition for finite vertex algebras
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Let L be a Lie pseudoalgebra, a in L. We show that, if a generates a (finite) solvable subalgebra S=<a>, then one may find a lifting a in S of [a] in S/S such that <a> is nilpotent. We then apply this result towards vertex algebras: we show that every finite vertex algebra V admits a decomposition into a semi-direct product V = U + N, where U is a subalgebra of V whose underlying Lie conformal algebra U^lie is a nilpotent self-normalizing subalgebra of V^lie, and N is a canonically determined ideal contained in the nilradical Nil V.
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In this paper, I investigate the ascending chain condition of right ideals in the case of vertex operator algebras satisfying a finiteness and/or a simplicity condition. Possible applications to the study of finiteness of orbifold VOAs is discussed.
In this paper we study the integral form of the lattice vertex algebra $V_L$. Based on the lattice structure, we introduce and study the associated modular vertex algebras $V_p$ and the quotient algebra $overline{V}_p$ as well as their irreducible modules over $mathbb Z_p$. We show that divided powers of general vertex operators preserve the integral lattice spanned by Schur functions indexed by partition-valued functions. We also show that the Garland operators, counterparts of divided powers of Heisenberg elements in affine Lie algebras, also preserve the integral form. These construe analogs of the Kostant $mathbb Z$-forms for the enveloping algebras of simple Lie algebras and the algebraic affine Lie groups in the situation of the lattice vertex algebras. We also prove that the irreducible modules (modulo Heisenberg generators of degree divisible by $p$) remain irreducible for the modular vertex algebra $overline{V}_p$.
I show that simple finite vertex algebras are commutative, and that the Lie conformal algebra structure underlying a reduced (i.e., without nilpotent elements) finite vertex algebra is nilpotent.
Quantum N-toroidal algebras are generalizations of quantum affine algebras and quantum toroidal algebras. In this paper we construct a level-one vertex representation of the quantum N-toroidal algebra for type C. In particular, we also obtain a level-one module of the quantum toroidal algebra for type C as a special case.
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