ORIENTED INVOLUTIONS AND SKEW-SYMMETRIC ELEMENTS IN GROUP RINGS
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Bibliographic record
Abstract
Let G be a group with involution * and σ : G → {±1} a group homomorphism. The map ♯ that sends α = ∑ α g g in a group ring RG to α ♯ = ∑ σ(g)α g g* 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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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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