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

**COMPUTING CONSTANTS IN SOME WEIGHT SUBSPACES**

OF FREE ASSOCIATIVE COMPLEX ALGEBRA

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

**Year:**2012

**Volume:**81

**Issue:**1