Scalar Actions

Lebow, A. ; Schreiber, M.

Canadian journal of mathematics, Tome 35 (1983) no. 4, pp. 750-768

Résumé

The subject of this paper arises from the familiar process whereby an automorphism of a field generates new representations from old. One may think of that process spatially, as a change of vector space structure in the representation space by means of the automorphism. The operators of the representation acting in the “new“ space then constitute the new representation. This point of view makes visible an algebraic structure we call a scalar action. A scalar action f of a ring R (with unity) in an abelian group Kis a ring homomorphism f:R → End(V) taking the unity element of R to the identity operator in End(V). If f is a scalar action of a field F and φ is an automorphism of F then f ∘ φ is another scalar action of F, and it is this construction which is used to define the “new” representation space mentioned above. But the variety of scalar actions goes rather beyond that construction.

Détail

DOI : 10.4153/CJM-1983-043-8

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