Abstract
In this paper, we first introduce a quantum $n$-space with a cocommutative Hopf algebra structure. Then it is shown that to this quantum $n$-space there corresponds a derivation algebra of $σ$-twisted derivations related to some algebra automorphisms $σ$ on the quantum $n$-space. Furthermore, we show that this derivation algebra is a noncommutative and non-cocommutative Hopf algebra, namely, a quantum group. Morever, for this the quantum $n$-space, we show how to construct a bicovariant differential calculus related to the derivation algebra.
Keywords
Quantum differential calculus
Quantum group
Noncommutative geometry
Quantum algebra
Hopf algebra
Quantum affine algebra
Mathematics
Algebra over a field
Pure mathematics
Filtered algebra
Cellular algebra
Universal enveloping algebra
Differential calculus
Quantum
Quantum spacetime
Automorphism
Operator algebra
Current algebra
Space (punctuation)
Algebra representation
Physics
Noncommutative quantum field theory
Quantum mechanics
Quantum gravity
Computer science
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
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