Homological Dimension And Tensor Identity Of Representations Of Quantum Algebras

Let A = Z[v]_? , where v is an indeterminate and (?) is the maximal ideal in Z [v] generated by v -1 and a fixed odd prime p.let A' =Q(v) is the fraction of A. U' is the quantum algebras over A' associated to (a_ij)_i,jⁿ, U'is a A'-Hopf algebra . Let U is the quantum algebras over A. Is a A subalgebra of U', U is also A - Hopf algebra with related structure. For an A- module M , let H(M) = F_δ(H(M)) , where H(M) = Hom_A(U,M) , LetH(A) = A[U],it is said to be a quantum coordinate algebras of U. This paper researchedthe relation of global dimension, weak dimension and Kull dimension of quantum algebras base ring A, proofed the homological dimension of those is 2.So we get pd_A[U](H(M))≤2 foran A - module M .We denote by C_f the category of A finite objects in C. In literature [2], proofed, for A free object of category C_f, the tensor identity of functor D set up. Using homological dimension, we introduced a subcategory C^f of C_f. We will proof for any object ofC^f (not a free object), tensor identity of functor D set up, i.e. (?)λ∈X⁺ and M∈C^f, we have a U - isomorphisms...