Sym(n)-and Alt(n)-modules with an additive dimension (Paris album no. 2)
Résumé
We revisit, clarify, and generalise classical results of Dickson and (much later) Wagner on minimal Sym(n)-and Alt(n)-modules. We present a new, natural notion of 'modules with an additive dimension' covering at once the classical, finitary case as well as modules definable in an o-minimal or finite Morley rank setting; in this context, we fully identify the faithful Sym(n)-and Alt(n)-modules of least dimension.
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