# IJPAM: Volume 81, No. 1 (2012)

COMPUTING CONSTANTS IN SOME WEIGHT SUBSPACES
OF FREE ASSOCIATIVE COMPLEX ALGEBRA

Milena Sosic
Department of Mathematics
University of Rijeka
2, Radmile Matejcic, Rijeka 51000, CROATIA

Abstract. Let be a fixed subset of nonnegative integers and let , be given complex numbers. We consider a free unital associative complex algebra generated by generators (each of degree one) together with linear operators , that act as twisted derivations on . The algebra is graded by total degree. More generally could be considered as multigraded. Then it has a direct sum decomposition into multigraded (weight) subspaces , where runs over multisets (over ). An element in is called a constant if it is annihilated by all operators . Then the fundamental problem is to describe the space of all constants in algebra . The space also inherits the direct sum decomposition into multigraded subspaces . Thus it is enough to determine the finite dimensional spaces .

AMS Subject Classification: 05Exx

Key Words and Phrases: q-algebras, noncommutative polynomial algebras, twisted derivations