PBW-deformations of quantum groups

JOURNAL OF ALGEBRA

卷:408

Article

Xu, Yongjun¹  Yang, Shilin¹ 

[1] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

关键词: PBW-deformation;    BGG-resolution;    Jacobi condition;    Quantum group;    Coideal subalgebra;    Root vector;    PBW basis;   

DOI  :  10.1016/j.jalgebra.2013.08.011

来源: Elsevier

【 摘 要 】

In this paper, we investigate certain deformations B-q(g) of the negative part U-q(-)(g) of quantized enveloping algebras U-q(g). An algorithm is established to determine when a given B-q(g) is a PBW-deformation of U-q(-)(g). For g of type A(2) and B-2, we classify PBW-deformations of U-q(-)(g). Moreover, we explicitly construct some PBW bases for a class of PBW-deformations B-q(g) of U-q(-)(g). As an application, lorgov-Klimyk's PBW bases for the no-standard quantum deformation U'(so(n,C)) of the unioversal enveloping algebra U(so(n,C)) are recovered. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free