Constructing Moduli Spaces of Low Dimensional A[Infinity]-Algebras by Extensions

Abstract

Infinity algebras are generalizations of associative and Lie algebras. An associative or Lie algebra has a product, which is a function that takes two inputs and gives one output, their product. Infinity algebras are functions which take any number of inputs and generate an output. These algebras have recently played an important role in mathematics and physics. This study examines extensions of infinity algebras and the differences between the theories of infinity algebras and their simpler associative and Lie counterparts.