Smooth SL(n, {C})-actions on (2_n-1)-manifolds were classified by Uchida [12], while smooth SL(2, {H})-actions on 7-manifolds are discussed in Abe [1]. In this paper, the classification of smooth actions of SL(n, {H}) and Sp(n, {C}) on simply connected closed (4_n-1)-manifolds is carried out for n ≥q 3.
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