Universal enveloping conformal algebras. (English) Zbl 1048.17017
Summary: The main objective of this paper is to study embeddings of Lie conformal algebras into associative conformal algebras. We prove that not all Lie conformal algebras admit such embeddings. However, in many important cases, including semisimple Lie conformal algebras of finite type, embeddings of this form exist and sometimes we can even describe universal enveloping associative conformal algebras of Lie conformal algebras and prove an analogue of the classical Poincaré-Birkhoff-Witt theorem.
MSC:
17B99 | Lie algebras and Lie superalgebras |
17B35 | Universal enveloping (super)algebras |
16S15 | Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) |
16S10 | Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |