nLab Weyl n-algebra

Idea

A concept of Weyl n-algebra is to be a refinement to higher algebra of the concept of Weyl algebra.

Definitions

Since ordinary Weyl algebras are universal enveloping algebras of Heisenberg Lie algebras of symplectic vector spaces (see here), and since there is a sensible notion of Heisenberg Lie $n$-algebra for all $n \in \mathbb{N}$, it makes sense to defines Weyl $n$-algebras to be the universal enveloping $E_n$-algebras of Heisenberg Lie $n$-algebras.

Another definition is considered by Markarian 2015.

References

• Nikita Markarian, Weyl $n$-algebras (arXiv:1504.01931)