Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum spaces with commutative coordinate algebras. This observation enables the realization of braiding mappings on commutative algebras. The aim of the article is to...

Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we first construct an infinite dimensional representation of the quantum matrix algebra Mq(3)(the coordinate ring of GLq(3)) and then use this representation to...

We study the q-Cli ord algebras Clq2(N; c ), called FRT{Cli ord algebras, introduced by Faddeev, Reshetikhin and Takhtajan. It is shown that Clq2(N; c ) acts on the q-exterior algebra (O q2 ). Moreover, explicit formulas for the embedding of Uq2(soN ) into Clq2(N; c ) and its relation to the vector and spin representations of Uq2(soN ) are given and proved. MSC 2000: 81R50, 15A66

We give a presentation of cyclotomic q-Schur algebras by generators and defining relations. As an application, we give an algorithm for computing decomposition numbers of cyclotomic q-Schur algebras. § 0. Introduction Let Hn,r be an Ariki-Koike algebra associated to a complex reflection group Sn ⋉ (Z/rZ). A cyclotomic q-Schur algebra Sn,r associated to Hn,r, introduced in [DJM], is defined as a...

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integer n, then H or H * is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd prime p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p. In recent years, there has been some progr...

The main goal is to study the Hopf algebra structure on quivers. The main result obtained by C. Cibils and M. Rosso is improved. That is, in the case of infinite dimensional isotypic components it is shown that the path coalgebra kQ admits a graded Hopf algebra structure if and only if Q is a Hopf quiver. All nonisomorphic point path Hopf algebras and point co-path Hopf algebras are found. The ...

The cocycle approach to topological charge algebras is generalized to the case of D-branes. The D-brane has two associated cocycles, with an anomalous term of the Noether charge algebra deriving from each. The resulting topological charge algebras are extensions of the standard, background superalgebra by two disjoint, commuting ideals. The formalism is applied to (p, q)-strings and the D-membr...

Clifford algebras are naturally associated with quadratic forms. These algebras are Z2 -graded by construction. However, only a Zn -gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V ) ↔ ∧ V and an ordering, guarantees a multivector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomor...

The main purpose of the present paper is to introduced notions (∈´,∈´∨q´)-UIFSSAs in subtraction BG-algebras. We provide different characterizations and some equivalent conditions terms level subsets It has been revealed that (q´,q´)-UIFSSA are (∈´,∈´)-UIFSSA but converse does not hold an example provided. (∈´,∈´∨q´)-UIFSIDs its usual properties. In addition, h−1(N˜[ς]) (∈´,∈´∨q´)-UIFSID. Moreo...