engleski

Some factorization in the twisted group algebra of symmetric groups

In this paper we will give a similar actorization 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 Sn on the polynomial ring Rn in n2 commuting variables Xab and also introduce a twisted group algebra (defined by the action of Sn on Rn) which we denote by A(Sn). 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.

symmetric group ; polynomial ring ; group algebra ; twisted group algebra

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