2006/07/26 by Vadim Schechtman · 1 voice
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.1007/0-8176-4478-4_18
openalex publication_date 2006/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
An algebra of differential operators is the enveloping algebra of a Lie algebroid T of vector fields. Similarly, a vertex algebra of differential operators is the enveloping algebra of a vertex algebroid, which is a Lie algebroid equipped with certain complementary differential operators. These operators should satisfy some complicated identities, these identities being a corollary of the Borcherd’s axioms of a vertex algebra. In this note we attempt to shed some light at the definition of a vertex algebroid, by proposing a new, equivalent definition which has nothing to do with the axioms of a vertex algebra and uses only classical objects such as complexes of De Rham, Hochschild and Koszul. This point of view works nicely for Calabi-Yau structures as well and opens the way to higher dimensional generalisations.