Anne Cortella, Jean-Pierre Tignol: The asymmetry of an anti-automorphism,

Submission: 2000, Sep 29

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.

2000 Mathematics Subject Classification: 11E39

Keywords and Phrases: anti-automorphism, central simple algebra, asymmetric pairings

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