Elizabeth Jurisich

Realizations of the three-point Lie algebra sl(2,ℛ) ⊕ (Ωℛ∕dℛ)

We describe the universal central extension of the three point current algebra sl(2,R) where R = C[t, t−1, u | u2 = t2 + 4t] and construct realizations of it in terms of sums of partial differential operators.

A Generalization of Lazard's Elimination Theorem

Abstract Using the classical Lazards elimination theorem, we obtain a decomposition theorem for Lie algebras defined by generators and relations of a certain type.

Representations of a∞ and d∞ with central charge 1 on the single neutral fermion Fock space

We construct a new representation of the infinite rank Lie algebra a∞ with central charge c = 1 on the Fock space of a single neutral fermion. We show that is a direct sum of irreducible integrable highest weight modules for a∞ with central charge c = 1. We prove that as a∞ modules is isomorphic to the Fock space F⊗1 of the charged free fermions. As a corollary we obtain the decompositions of certain irreducible highest weight modules for d∞ with central charge into irreducible highest weight modules for d∞ with central charge c = 1.

A Wakimoto Type Realization of Toroidal 𝔰𝔩n+1

The authors construct a Wakimoto type realization of toroidal 𝔰𝔩n+1. The representation constructed in this paper utilizes non-commuting differential operators acting on the tensor product of two polynomial rings in infinitely many commuting variables.

Lie Algebras, Vertex Operator Algebras, and Related Topics

We discuss some applications of fusion rules and intertwining operators in the representation theory of orbifolds of triplet vertex algebras. We prove that the classification of irreducible modules for vertex algebra

The 3-point Virasoro algebra and its action on a Fock space

W(p) ^{;A_m};

A resolution for standard modules of Borcherds Lie algebras

follows from (conjectural) fusion rules from singlet vertex algebra. In the case of

Determination of the 2- cocycles for the three point Witt algebra

p=2

The three point gauge algebra

we rigorously prove fusion rules formulas in the framework of vertex algebras and intertwining operators, so our result gives a classification of modules for

\mathcal V\ltimes \mathfrak{sl}(2, \mathcal R) \oplus\left(\Omega_{\mathcal R}/d{\mathcal R}\right)

W(p)^{;A_m};