The Straightening Identity in the Universal Enveloping Algebra of the Heisenberg Algebra

Abstract

This work aims to formulate and prove the nontrivial straightening identity in the universal enveloping algebra of the Heisenberg algebra. This identity is a special case of the Baker-Campbell-Hausdorff formula, but was proven using a new proof method of double induction. This general formula is applicable for straightening identities in many different Lie algebras, one application being the Onsager algebra of sl₄.