Glasnik Matematicki, Vol. 51, No. 1 (2016), 1-15.

SOME FACTORIZATIONS IN THE TWISTED GROUP ALGEBRA OF SYMMETRIC GROUPS

Milena Sošić

Abstract.   In this paper we will give a similar factorization as in [3,4], where Svrtan and Meljanac examined certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative algebra of noncommuting polynomials equipped with multiparametric partial derivatives. In order to replace these matrix factorizations (given from the right) by twisted algebra computation, we first consider the natural action of the symmetric group S_n on the polynomial ring R_n in n² commuting variables X_a,b and also introduce a twisted group algebra (defined by the action of S_n on R_n) which we denote by A(S_n). Here we consider some factorizations given from the left because they will be more suitable in calculating the constants (= the elements which are annihilated by all multiparametric partial derivatives) in the free algebra of noncommuting polynomials.

2010 Mathematics Subject Classification.   05E15.

Key words and phrases.   Symmetric group, polynomial ring, group algebra, twisted group algebra.

DOI: 10.3336/gm.51.1.01

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