Equality of elementary linear and symplectic orbits with respect to an alternating form

JOURNAL OF ALGEBRA

卷:451

Article

Chattopadhyay, Pratyusha¹  Rao, Ravi A.² 

[1] Indian Stat Inst, Stat & Math Unit, Bangalore 560059, Karnataka, India

[2] Tata Inst Fundamental Res, Dr Homi Bhabha Rd, Bombay 400005, Maharashtra, India

关键词: Unimodular rows;    Symplectic group;    Group action;    Transvections;   

DOI  :  10.1016/j.jalgebra.2015.12.001

来源: Elsevier

【 摘 要 】

An elementary symplectic group w.r.t. an invertible alternating matrix is defined. It is shown that the group of symplectic transvections of a symplectic module coincides with this elementary symplectic group in the free case. Equality of orbit spaces of a unimodular element under the action of the linear group, symplectic group, and symplectic group w.r.t. an invertible alternating matrix is established. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free