Knit products of graded Lie algebras and groups
  If a graded Lie algebra is the direct sum of two graded sub Lie algebras, its bracket can be written in a form that mimics a "double sided semidirect product". It is called the {\it knit product} of the two subalgebras then. The integrated version of this is called a {\it knit product} of groups --- it coincides with the {\it Zappa-Sz\'ep product}. The behavior of homomorphisms with respect to knit products is investigated. 
Peter W. Michor