The asymmetry of an anti-automorphism

Cortella, Anne;Tignol, Jean-Pierre
(2002) Journal of Pure and Applied Algebra — Vol. 167, n° 2-3, p. 175-193 (2002)

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Abstract
The asymmetry of a nonsingular pairing on a vector space is an endomorphism of the space on which the classification of arbitrary pairings (not necessarily symmetric or skew-symmetric) is based. A general notion of asymmetry is defined for arbitrary anti-automorphisms on a central simple algebra, and conditions are given to characterize the elements which are the asymmetries of some anti-automorphism. The asymmetry is used to define the determinant of an anti-automorphism.
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Cortella, A., & Tignol, J.-P. (2002). The asymmetry of an anti-automorphism. Journal of Pure and Applied Algebra, 167(2-3), 175-193. https://doi.org/10.1016/S0022-4049(01)00029-9 (Original work published 2002)