IJPAM: Volume 81, No. 1 (2012)
OF FREE ASSOCIATIVE COMPLEX ALGEBRA
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 .
Received: August 14, 2012
AMS Subject Classification: 05Exx
Key Words and Phrases: q-algebras, noncommutative polynomial algebras, twisted derivations
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395