An algebra homomorphism ψ from the q-deformed algebra U q (iso 2) with generating elements I, T 1 , T 2 and defining relations [I, T 2 ] q = T 1 , [T 1 , I] q = T 2 , [T 2 , T 1 ] q = 0 (where [A, B] q = q 1/2 AB − q −1/2 BA) to the extensionˆU q (m 2) of the Hopf algebra U q (m 2) is constructed. The algebra U q (iso 2) at q = 1 leads to the Lie algebra iso 2 ∼ m 2 of the group ISO(2) of motio...

Some Realization of gl q (n)-covariant Oscillator Algebra and gl q (n)-covariant q-Virasoro Algebra with q a root of unity. Abstract In this paper some realization of gl q (n)-covariant oscillators is obtained when q is a root of unity. And the gl q (n)-covariant q-Virasoro algebra is presented by using the gl q (n)-covariant oscillators.

We study a q-analog Qr(n, q) of the partition algebra Pr(n). The algebra Qr(n, q) arises as the centralizer algebra of the finite general linear group GLn(Fq) acting on a vector space IR q coming from r-iterations of Harish-Chandra restriction and induction. For n ≥ 2r, we show that Qr(n, q) has the same semisimple matrix structure as Pr(n). We compute the dimension dn,r(q) = dim(IR r q ) to be...

where β = q+q and δ = −(q − q) 2 . (TD) can be regarded as a q-analogue of the DolanGrady relations and we call A the q-Onsager algebra. We classify the finite-dimensional irreducible representations of A. All such representations are explicitly constructed via embeddings of A into the Uq(sl2)-loop algebra. As an application, tridiagonal pairs of qRacah type over C are classified in the case wh...

the aim of this paper is to introduce the notions of ($epsilon, epsilon vee q$)-fuzzy p-ideals, ($epsilon, epsilon vee q$)-fuzzy q-ideals and ($epsilon, epsilon vee q$)-fuzzy a-ideals in bcialgebras and to investigate some of their properties. several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of bci-algebras i...

We study a class of endomomorphism algebras of certain q-permutation modules over the Hecke algebra of type B, whose summands involve both parabolic and quasi-parabolic subgroups, and prove that these algebras are integrally free and quasi-hereditary, and are stable under base change. Some consequences for decomposition numbers are discussed. The notion of a q-Schur algebra was introduced by Di...

We show that the Faddeev-Pyatov SL q (N) differential algebra [1] is a subalgebra of the GL q (N) differential algebra constructed by Schupp, Watts and Zumino [2]. In the paper [1], the bicovariant differential algebra on SL q (N) (see below (10), (11)) with generators {T ij , L ij , ˜ Ω ij } i, j = 1,. .. N has been constructed. The elements T ij are generators of the algebra F un(SL q (N)), w...