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The Campbell-Hausdorff group and a polar decomposition of graded algebra automorphisms

1988
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Pacific Journal of Mathematics
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Let A = nj°e£ 0 gΓfc(Λ) be a complete graded (associative or Lie) algebra over a field of characteristic zero, filtered by the decreasing filtration Fj(A) = Π^L, & k (A). We let Aut(Λ) denote the group of filtration preserving automorphisms of A, and Aut o (Λ) the subgroup consisting of those elements of AuX(A) which preserve the grading. In this paper we prove that every element of Aut(A) has a unique polar decomposition of the form u 0 exp(d), where u 0 e Aut o (A) and d :A -> A is a

doi:10.2140/pjm.1988.131.219
fatcat:42jsyvosmva3tjub2msv7sthdq