GLq(N)-Covariant Quantum Algebras and Covariant Differential Calculus

Abstract

We consider GLq(N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with q-deformed commutation and q-deformed anticommutation relations. The connection with the bicovariant differential calculus on the linear quantum groups is disscussed.

13 pages, Dubna Preprint JINR E2-92-477

References in corpus (3)

• Differential Geometry on Linear Quantum Groups
• Paragrassmann Analysis and Quantum Groups
• Deformed Traces and Covariant Quantum Algebras for Quantum Groups $G{L}_{qp}(2)$ and $G{L}_{qp}(1|1)$

Cited by in corpus (9)

• Covariant differential complexes on quantum linear groups
• On Paragrassmann Differential Calculus
• On the algebraic structure of differential calculus on quantum groups
• Weyl approach to representation theory of reflection equation algebra
• Quantum group covariant noncommutative geometry
• GL_q(N)-covariant braided differential bialgebras
• Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
• Interrelations between Quantum Groups and Reflection Equation (Braided) Algebras
• On Poisson-Lie structure on the external algebra of the classical Lie groups