A quantum space and some associated quantum groups
Muttalip \"Ozav\c{s}ar

TL;DR
This paper introduces a quantum n-space with a Hopf algebra structure, constructs a related derivation algebra as a quantum group, and develops a bicovariant differential calculus on it.
Contribution
It constructs a new quantum n-space with a Hopf algebra structure and establishes its associated derivation algebra as a noncommutative quantum group, along with a differential calculus.
Findings
Quantum n-space with Hopf algebra structure introduced.
Derivation algebra shown to be a noncommutative quantum group.
Bicovariant differential calculus constructed for the quantum n-space.
Abstract
In this paper, we first introduce a quantum -space with a cocommutative Hopf algebra structure. Then it is shown that to this quantum -space there corresponds a derivation algebra of -twisted derivations related to some algebra automorphisms on the quantum -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 -space, we show how to construct a bicovariant differential calculus related to the derivation algebra.
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