TL;DR
This paper explores the structure of quantum Anti-de Sitter space and its associated quantum groups, establishing relationships between quantum groups and algebras, and introducing differential calculus on quantum AdS space.
Contribution
It presents methods to derive the quantum AdS group from quantum orthogonal groups and develops differential calculus with reality conditions on quantum AdS space.
Findings
Quantum AdS algebra derived from quantum group conjugation
Explicit relationships between quantum group and algebra established
Differential calculus on quantum AdS space formulated
Abstract
The quantum Anti-de Sitter (AdS) group and quantum AdS space is discussed. Ways of getting the quantum AdS group from real forms of quantum orthogonal group are presented. Differential calculus on the quantum AdS space are also introduced. In particular, reality of differential calculus are given. We set up explicit relationships between quantum group and quantum algebra, which can be refereed as the quantum counterpart of the classical exponential. By this way, quantum AdS algebra is deduced from conjugation on the quantum AdS group.
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