Developing a new L-infinity algebra using symmetric brace algebras

Exploring the connections between Linfinity algebras and symmetric brace algebras is a relatively recent area of study. Linfinity algebras are the skew symmetric analog of Ainfinity algebras. The latter structures allow for a transfer of associativity from a DG-algebra to a homotopic DG-module. Symmetric braces can greatly simplify the calculations involved in proving an L infinity structure. We will investigate how to find a new L infinity algebra structure when given an existing L infinity structure and a collection of maps {fi} with relations that coincide with the definition of an L infinity morphism, all within the context of symmetric brace algebra notation.