Abstract
Let G be a group with involution * and σ : G → {±1} a group homomorphism. The map ♯ that sends α = ∑ αgg in a group ring RG to α♯ = ∑ σ(g)αgg* is an involution of RG called an oriented group involution. An element α ∈ RG is symmetric if α♯ = α and skew-symmetric if α♯ = -α. The sets of symmetric and skew-symmetric elements have received a lot of attention in the special cases that * is the inverse map on G or σ is identically 1, while the general case has been almost ignored. In this paper, we determine the conditions under which the set of elements that are skew-symmetric relative to a general oriented involution form a subring of RG. This is the sequel to another paper where the analogous problem for the symmetric elements was studied, with a small oversight that is corrected here.
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