Differential Geometry on Linear Quantum Groups

Abstract

An exterior derivative, inner derivation, and Lie derivative are introduced on the quantum group $G{L}_q(N)$. $S{L}_q(N)$ is then found by constructing matrices with determinant unity, and the induced calculus is found.

15 pages

Cited by in corpus (48)

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• $h$-Deformation as a Contraction of $q$-Deformation
• Bicovariant Quantum Algebras and Quantum Lie Algebras
• Nonabelian Phenomena on D-branes
• Vector Fields on Quantum Groups
• The Lagrangian of q-Poincare' Gravity
• The quantum de Rham complexes associated with $S{L}_h(2)$
• Quantum Group Gauge Theories and Covariant Quantum Algebras
• Characteristic Relations for Quantum Matrices
• GLq(N)-Covariant Quantum Algebras and Covariant Differential Calculus
• Spectral extension of the quantum group cotangent bundle
• A Class of Bicovariant Differential Calculi on Hopf Algebras
• Covariant differential complexes on quantum linear groups
• Quantum groups and deformed special relativity
• Representations and Clebsch-Gordan coefficients for the Jordanian quantum algebra U_h(sl(2))
• On the algebraic structure of differential calculus on quantum groups
• Bicovariant differential geometry of the quantum group GL_q(3)
• Weyl approach to representation theory of reflection equation algebra
• Quantum group covariant noncommutative geometry
• Induced extended calculus on the quantum plane
• $S{U}_q(2)$ Lattice Gauge Theory
• Standard Complex for Quantum Lie Algebras
• Bicovariant Differential Geometry of the Quantum Group $S{L}_h(2)$
• Cartan calculi on the quantum superplane
• Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
• Toward a q-Deformed Standard Model
• Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
• q-Deformed su(2) instantons by q-quaternions
• Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
• q-Quaternions and q-deformed su(2) instantons
• On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N
• $q$-Deformed Chern Characters for Quantum Groups $S{U}_q(N)$
• Quantum Groups, Non-Commutative Differential Geometry and Applications
• Interrelations between Quantum Groups and Reflection Equation (Braided) Algebras
• Nonstandard Poincare and Heisenberg Algebras
• Differential calculus on quantum groups: Constructive procedure
• All bicovariant differential calculi on Glq(3,C) and SLq(3,C)
• On construction of unitary quantum group differential calculus
• Implications of the Hopf algebra properties of noncommutative differential calculi
• Generalization of Weyl realization to a class of Lie superalgebras
• q-Deformed quaternions and su(2) instantons
• The quantum Cartan algebra associated to a bicovariant differential calculus
• Gauge transformations and quasitriangularity
• Differential Calculi of Poincare-Birkhoff-Witt type on Universal Enveloping Algebras
• On Poisson-Lie structure on the external algebra of the classical Lie groups