Tensor product of modules over a Lie conformal algebra

TL;DR

This paper establishes conditions for the existence of tensor products of modules over Lie conformal algebras, provides algebraic constructions, and explores their properties including commutativity.

Contribution

It introduces necessary and sufficient conditions for tensor products over Lie conformal algebras and offers two algebraic constructions.

Findings

Tensor product existence characterized by specific conditions

Two algebraic constructions of tensor products provided

Tensor product shown to be commutative

Abstract

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and conformal linear maps. We prove commutativity of the tensor product.