Some Quantum Vertex Algebras of Zamolodchikov–faddeev Type

Abstract

This is a continuation of a previous study of quantum vertex algebras of Zamolodchikov-Faddeev type. In this paper, we focus our attention on the special case associated to diagonal unitary rational quantum Yang-Baxter operators. We prove that the associated weak quantum vertex algebras, if not zero, are irreducible quantum vertex algebras with a normal basis in a certain sense.

Twisted modules for quantum vertex algebras

“…The main result of this paper naturally generalizes the corresponding results of [11,2]. As an application we construct and classify irreducible twisted modules for quantum vertex algebras V Q which were constructed in [13] from a multiplicative skew complex matrix Q.…”

“…It was proved in [13] (cf. [3]) that there exists a unique quantum vertex algebra structure on V Q with 1 as the vacuum vector and with Y (u (i) , z) = X i (z), Y (v (i) , z) = Y i (z) for 1 ≤ i ≤ r.…”

“…In this section we shall use the general construction we have established in Section 3 to construct twisted modules for quantum vertex algebras V Q which were constructed in [13].…”

“…First we recall the quantum vertex algebra V Q from [13]. Let r be a positive integer and let Q = (q ij ) r i,j=1 be a square matrix of complex numbers such that…”

Associating quantum vertex algebras to deformed Heisenberg Lie algebras

“…In Lemma 4 below, we shall prove that for nonzero ∈ C, every (nonzero) vacuum L-module of level is irreducible. Then by [9,Proposition 2.11], VB q ( , 0) is an irreducibleB q -module. It follows that VB q ( , 0) as a (left) VB q ( , 0)-module is irreducible.…”