On Zhu's algebra and C2–algebra for symplectic fermion vertex algebra SF(d)+

Symplectic Fermions – Symmetries of a Vertex Operator Algebra

The model of d symplectic fermions constructed by Abe [1] gives an example of a C2cofinite vertex operator algebra admitting logarithmic modules. While the case d = 1 is a rigorous formulation of the well known triplet algebra, the case d > 1 has not yet been analyzed from the perspective of W-algebras. It is shown that in the latter case the W(2, 2 2−d−1, 3 2+d)-algebra is realized. With respe...

Recursive Fermion System in Cuntz Algebra . I — Embeddings of Fermion Algebra into Cuntz Algebra —

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra O2 (or O2d more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of O2 is constructed explicitly. Generalizing this construction to the case of O2p , an embedding of CAR onto the U(1)-invariant subalgebra of...

The Brauer Algebra and the Symplectic Schur Algebra

Let k be an algebraically closed field of characteristic p > 0, let m, r be integers with m ≥ 1, r ≥ 0 and m ≥ r and let S0(2m, r) be the symplectic Schur algebra over k as introduced by the first author. We introduce the symplectic Schur functor, derive some basic properties of it and relate this to work of Hartmann and Paget. We do the same for the orthogonal Schur algebra. We give a modified...

Vertex Operator Algebra Structure of Standard Affine Lie Algebra Modules

On dimensions of derived algebra and central factor of a Lie algebra

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.