ࡱ > C E B D bjbjVV -" < < a 8 ? , k ) N " +) -) -) -) -) -) -) $ , . Q) ! b @ Q) r) ]! ]! ]! f +) ]! +) ]! ]! r ' T ( @W~
j ' ) ) 0 ) ' 6/ U 6/ ( 6/ ( " ]! Q) Q) ) 6/ : C O M P U T I N G C O N S T A N T S I N S O M E S U B S P A C E S O F F R E E U N I T A L A S S O C I A T I V E C O M P L E X A L G E B R A
M i l e n a S O `I ,
D e p a r t m e n t o f M a t h e m a t i c s , U n i v e r s i t i y o f R i j e k a , O m l a d i n s k a 1 4 , 5 1 0 0 0 R i j e k a , C r o a t i a
W e c o n s i d e r a f r e e u n i t a l a s s o c i a t i v e c o m p l e x a l g e b r a B g e n e r a t e d b y N generators, each of degree one. We equip B with a multiparametric qij-differential structure given by N linear operators, which generalise partial derivatives. The algebra B is graded by total degree. More generally B could be considered as multigraded. Then it has a direct sum decomposition into multigraded (weight) subspaces BQ, where Q runs over multisets (over N ). When Q is a set, the associated weight subspace BQ is called generic, otherwise BQ is called degenerate. An element C in B is called a constant if it is annihilated by all generalized partial derivatives. Then the main problem is to describe the space of all constants in B. By using the decomposition of B into multigraded weighted subspaces BQ the main problem reduces to finding constants in each BQ. Up to total degree equal to four we give explicit formulas for basic constants in BQ. Depending on the actual (singular) values of parameters qijs the number of basic constants in BQ many vary as well.
REFERENCES
1. Fronsdal C.: On the classification of q-algebras, math.QA/0003146 v1 24 Mar 2000
2. Fronsdal C. and Galindo A.: The ideals of free differential algebras, J. Algebra 222 (1999), 708-746 (math.QA/9806069 v2 17 Nov 1999).
3. Meljanac S., Perica A. and Svrtan D.: The energy operator for a model with a multipara-metric infinite statistics, J. Phys. A36 no. 23 (2003), 6337-6349.
4. Meljanac S. and Svrtan D.: Determinants and inversion of Gramm matrices in Fock representation of qkl - canonical commutation relations and applications to hyperplane arrangements and quantum groups. Proof of an extension of Zagiers conjecture (math-ph/0304040 v1 26 Apr 2003).
5. Zagier D.: Realizability of a model in infinite statistics, Commun. Math. Phys. 147 (1992), 199-210.
Abstract: MATH/CHEM/COMP 2011, Dubrovnik, June 13-18, 2011
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