English

Sym(n)- and Alt(n)-modules with an additive dimension

Group Theory 2021-11-24 v1 Logic Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2111.11498,
  title  = {Sym(n)- and Alt(n)-modules with an additive dimension},
  author = {Luis Jaime Corredor and Adrien Deloro and Joshua Wiscons},
  journal= {arXiv preprint arXiv:2111.11498},
  year   = {2021}
}
R2 v1 2026-06-24T07:48:01.967Z