# The Relation between constants in generic and degenerate subspaces of free unital associative complex algebra

### Abstract

From the study of the constants in the generic and the degenerate weight subspaces of the free unitary associative complex algebra * B*, it follows that the constants in the degenerate weight subspaces of the algebra

*can be constructed from the corresponding constants in the generic case by a certain specialization procedure. Here we consider that each constant in each generic weight subspace of the algebra*

**B***can be expressed by certain iterated*

**B***-commutators.*

**q**### References

[2] C. Frønsdal, On the classification of q-algebras, Lett. Math. Phys. 53 No.2 (2000) 105-120.

[3] C. Frønsdal, A. Galindo, The ideals of free differential algebras, J. Algebra 222 (1999) 708-746.

[4] S. Meljanac, A. Perica, D. Svrtan, The energy operator for a model with a multiparametric infinite statistics, J. Phys., A36 23 (2003) 6337-6349.

[5] S. Meljanac, D. Svrtan, Study of Gram matrices in Fock representation of multiparametric canonical commutation relations, extended Zagier's conjecture, hyperplane arrangements and quantum groups, Math. Commun. 1 (1996) 1-24.

[6] M. Sošić, Computation of constants in multiparametric quon algebras. A twisted group algebra approach. Math. Commun. 22 No.2, (2017) 177-192

[7] M. Sošić, Computing constants in some weight subspaces of free associative complex algebra, Int. J. Pure Appl. Math., Vol.81 (1) (2012) 165-190.

[8] D. Stanton, Constructive Combinatorics, UTM, Springer (1986).