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Lie Action of Certain Skews in *-Rings
Published online by Cambridge University Press: 20 November 2018
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A *-ring is an associative ring R with an anti-automorphism * of period 2 (involution). Call x ∈ R skew (symmetric) if x = - x* (x = x*) and let K(S) be the additive subgroup of all skews (symmetries). If [a, b] denotes the Lie product of a, b ∈ R (that is, ab — ba) and if [A, B] denotes the Lie product of the additive subgroups A and B of R (that is, the additive subgroup generated by [a, b], a and b ranging over A and B) then clearly [K, K] is an additive subgroup contained in K.
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- Copyright © Canadian Mathematical Society 1978
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