JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 65-74.doi: 10.6040/j.issn.1671-9352.0.2019.540

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PBW-deformations of type B2 quantum group and their symmetry property

REN Xiao-qian1, XU Yong-jun1,2*   

  1. 1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China;
    2.School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2020-07-14

Abstract: 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 A2 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 B2 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 B2 quantum group and investigate their symmetry property, i.e., all the symmetric PBW-deformations of type B2 quantum group under four kinds of involution anti-automorphisms are obtained.

Key words: quantum group, connected graded algebra, symmetric PBW-deformation, complexity, Jacobi conditions

CLC Number: 

  • O152.1
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