Ben Cox

n-Point Virasoro algebras and their modules of densities

In this paper we introduce and study

Quantum Deformations of Imaginary Verma Modules

n

Intermediate Wakimoto modules for affine

-point Virasoro algebras,

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

\tilde{\W_a}

DJKM algebras and non-classical orthogonal polynomials

, which are natural generalizations of the classical Virasoro algebra and have as quotients multipoint genus zero Krichever-Novikov type algebras. We determine necessary and sufficient conditions for the latter two such Lie algebras to be isomorphic. Moreover we determine their automorphisms, their derivation algebras, their universal central extensions, and some other properties. The list of automorphism groups that occur is

DJKM ALGEBRAS I: THEIR UNIVERSAL CENTRAL EXTENSION

C_n

Simple superelliptic Lie algebras

,

Representations of quantum groups defined over commutative rings

D_n

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

,

A Wakimoto Type Realization of Toroidal 𝔰𝔩n+1

A_4