Real Forms of Complex Quantum Anti de Sitter Algebra Uq (Sp(4,C)) and their Contraction Schemes

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We describe four types of inner involutions of the Cartan-Weyl basis providing (for |q|=1 and q real) three types of real quantum Lie algebras: Uq(O(3,2)) (quantum D=4 anti-de-Sitter), Uq(O(4,1)) (quantum D=4 de-Sitter) and Uq(O(5)). We give also two types of inner involutions of the Cartan-Chevalley basis of Uq(Sp(4;C)) which can not be extended to inner involutions of the Cartan-Weyl basis. We outline twelve contraction schemes for quantum D=4 anti-de-Sitter algebra. All these contractions provide four commuting translation generators, but only two (one for |q|=1, second for q real) lead to the quantum algebra with an undeformed space rotations O(3) subalgebra.