Connectedness of some fibres on a compact connected Lie group

Alexander Markus, Tin Yau Tam

Research output: Contribution to journalArticlepeer-review


Given a compact connected Lie group G with Lie algebra g, we prove the connectedness of the fibres for the following two maps: (1) πA: G → t defined by g → π(Ad(g)A), A ε g, where t is a Cartan subalgebra of g and π: g → is the orthogonal projection with respect to the G-invariant inner product 〈·,·〉 on g. (2) ξA,C: G → ℝ defined by g → 〈Ad (g)A, C〉 A, Cεg. As a corollary of (2), we obtain a new proof of the convexity theorem in Tam [T.Y. Tam, Convexity of generalized numerical range associated with a compact Lie group, J. Austral. Math. Soc. 70 (2002), pp. 57-66].

Original languageEnglish
Pages (from-to)1121-1126
Number of pages6
JournalLinear and Multilinear Algebra
Issue number10
StatePublished - 1 Oct 2011


  • C-numerical range
  • Compact connected Lie group
  • Connectedness

ASJC Scopus subject areas

  • Algebra and Number Theory


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