| Quantum group theory is a very important research content, which is a very important branch of algebra developed in the mid-eighties of last century. Since the last three decades, its theories have been widely discussed. The aim of this thesis is to study the isomorphism and automorphis-m of quantized enveloping algebra of the Lie superalgebra osp(1,2) when q is not root of unit. Quantized enveloping algebra Uq (osp(1,2)) is generated by the four variables E,F,K,K-1with the relations:Explicitly, in the first part, we introduce the research background of quantized enveloping alg-ebra of the Lie superalgebra osp(1,2) when q is not root of unit, and further lead to the object of study in this paper:the isomorphism and automorphism of Uq (osp(1,2)).In the second part, we list some of the main results of U (osp(1,2)):Uq (osp(1,2)) admits a super hopf algebra structure(lemma1.4); The center Z(Uq (osp(1,2))) generated by the casimir element Cq is a subalgebra of Uq (osp(1,2))(lemma1.5); We get the equalities that the gen-erators of Uq(osp(1,2)) satisfy by induction(lemmal.6); Uq(osp(1,2)) is a Notherian ring with a basis {FiKlEj|i,j∈N,l∈Z}(lemma1.7); The classifications of all finite-dimensional si-mple module are given clearly (lemma1.8).In the third part, we mainly discuss the isomorphism between quantized enveloping algebra Uq(osp(1,2)) and Up (osp(1,2)), the following are the main conclusions: Lemma2.1An element u∈Uq(osp(1,2)) is multiplicative invertiable if and only if there exist λ∈C*,m∈Z such that u=λK"..Theorem2.3Suppose p,q∈C*is not a root of unity in a field C,then Uq(osp(1,2)) and Up(osp(1,2))are isomorphism as C-algebras if and only if p=q±1.In the last part,we mainly discuss the automorphism of Uq(osp(1,2)),the main conclusi-on is:Theorem3.1Suppose q∈C*and q is not a root of unity in a field C,then φ∈Aut(Uq(osp(1,2)))if and only if(1)φK)=K,φ(E)=λEKr,φ(F)=λ-1K-rF, or(2)φ(K)=-K,φ(E)=λEKr,φ(F)=-λ-1K-rF... |
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