Extending structures for associative conformal algebras

Abstract

In this paper, we give a study of the $\mathbb{C}[\partial ]$-split extending structures problem for associative conformal algebras. Using the unified product as a tool, which includes interesting products such as bicrossed product, cocycle semi-direct product and so on, a cohomological type object is constructed to characterize the $\mathbb{C}[\partial ]$-split extending structures for associative conformal algebras. Moreover, using this theory, the extending structures of an associative conformal algebra $A$ which is free as a $\mathbb{C}[\partial ]$-module by the $\mathbb{C}[\partial ]$-module $Q=\mathbb{C}[\partial ]x$ are described using flag datums of $A$. Furthermore, we give a classification of the extending structures of $A$ by $Q=\mathbb{C}[\partial ]x$ in detail up to equivalence when $A$ is a free associative conformal algebra of rank 1.

17 pages, Linear and Multillinear Algebra, 2017

References in corpus (1)

• Simple associative conformal algebras of linear growth