Scholarlink

In this chapter we first define the symplectic, orthogonal and unitary groups. Building on work of Britnell and Milnor, we then give necessary and sufficient criteria for an element X of the general linear group \({\mathrm {GL}}(V)\) to preserve a non-degenerate alternating, hermitian or quadratic form on V , in terms of the elementary divisors of \(\,X\) .

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Preliminaries on Classical Groups

  • 章节

  • 发表日期：

    2025年

查看全文
  • Giovanni De Franceschi,
  • Martin W. Liebeck,
  • Eamonn A. O’Brien

摘要

In this chapter we first define the symplectic, orthogonal and unitary groups. Building on work of Britnell and Milnor, we then give necessary and sufficient criteria for an element X of the general linear group \({\mathrm {GL}}(V)\) to preserve a non-degenerate alternating, hermitian or quadratic form on V , in terms of the elementary divisors of \(\,X\) .