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}
}