Quadratic-linar algebras associated with factorizations of   noncommutative polynomials and noncommutative differential polynomials
  This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and differential polynomials. Such algebras posses a natural derivation and give us a new understanding of a nature of noncommutative symmetric functions. 
Israel Gelfand, Vladimir Retakh, Robert Lee Wilson