On associative conformal algebras of linear growth II

Simple Associative Conformal Algebras of Linear Growth

We describe simple finitely generated associative conformal algebras of Gel’fand–Kirillov dimension one.

Associative Algebras Related to Conformal Algebras

In this note, we introduce a class of algebras that are in some sense related to conformal algebras. This class (called TC-algebras) includes Weyl algebras and some of their (associative and Lie) subalgebras. By a conformal algebra we generally mean what is known as H-pseudo-algebra over the polynomial Hopf algebra H = k[T1, . . . , Tn]. Some recent results in structure theory of conformal alge...

The associative algebras of conformal field theory

Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a deformation of the latter. Alternatively, it can be described as an associative quotient of the algebra given by a modified normal ordered product. We clarify the r...

Non Associative Linear Algebras

Associative Conformal Algebras with Finite Faithful Representation

The notion of conformal algebra appears as an algebraical language describing singular part of operator product expansion (OPE) in conformal field theory [BPZ]. Explicit algebraical exposition of this theory leads to the notion of vertex (chiral) algebra (see, e.g., [B], [DL], [FLM]). Roughly speaking, conformal algebras correspond to vertex algebras by the same way as Lie algebras correspond t...