%A REN Xiao-qian, XU Yong-jun
%T PBW-deformations of type *B*_{2} quantum group and their symmetry property
%0 Journal Article
%D 2020
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2019.540
%P 65-74
%V 55
%N 8
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3319.shtml}
%8
%X The negative parts of quantum groups are very important connected graded algebras appeared in the quantum group theory. Their PBW-deformations are called the PBW-deformations of quantum groups. Except the *A*_{}2 case, the defining relations of these algebras are homogeneous quantum Serre relations with mixed degrees. In particular, the defining relations of the negative part of type *B*_{2} quantum group are respectively the homogeneous quantum Serre relations with degree 3 and 4. In this paper, in the framework of PBW-deformations of connected graded algebras, we explicitly characterize all the PBW-deformations of type *B*_{2} quantum group and investigate their symmetry property, i.e., all the symmetric PBW-deformations of type *B*_{2} quantum group under four kinds of involution anti-automorphisms are obtained.