Remark

Under the hypotheses of the cor. of prop. 8, suppose in addition that A be a field and that E be of finite dimension over A. Let ω be an endomorphism of E, ω_1 and ω_2 its right and left adjoints. Each of the conditions ωω_1 = 1, ωω_2 = 1, ω_1ω = 1, ω_2ω = 1 entails that ω is an automorphism of E leaving Φ invariant, and that ω_1 = ω_2.