Abstract
Noncommutative derivative operators acting on the quantum 3D space in the sense of Manin are introduced. Furthermore, the quantum 3D space is extended by the series expansion of the logarithm of the grouplike generator in the quantum 3D space. We give its differential calculus and the corresponding Weyl algebra. We also obtain algebra of Cartan–Maurer forms on this extension and the corresponding Lie algebra of vector fields. All noncommutative results are found to reduce to those of the standard commutative algebra when the deformation parameter of the quantum 3D space is set to one.
Keywords
Quantum differential calculus
Noncommutative geometry
Mathematics
Differential calculus
Algebra over a field
Weyl algebra
Pure mathematics
Filtered algebra
Noncommutative quantum field theory
Universal enveloping algebra
Noncommutative algebraic geometry
Multivector
Subalgebra
Quantum spacetime
Algebra representation
Quantum
Cellular algebra
Quantum mechanics
Physics
Quantum gravity
Subject Areas
Algebraic structures and combinatorial models
·Geometry and Topology ·Physical Sciences
Advanced Topics in Algebra
·Algebra and Number Theory ·Physical Sciences
Advanced Operator Algebra Research
·Mathematical Physics ·Physical Sciences
Citations by Year
2012: 1
2014: 1
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