The research aims to construct the canonical vertex extension of the Atiyah algebra of differential one-forms in a coordinate-free manner.
Used tools of differential calculus for construction
Applied the concepts of vertex algebroids
Focused on the Atiyah algebra of differential forms
Developed an explicit coordinate-free framework for the canonical vertex extension
Demonstrated the applicability of differential calculus tools in the construction
Clarified the relationship between the vertex algebroid and differentiable structures
Abstract
We present an explicit coordinate-free construction of the canonical vertex extension of the Atiyah algebra of the sheaf of differential one-forms using standard tools of differential calculus.