Makar-Limanov's symmetric free subalgebra conjecture for division rings with involution
Makar-Limanov's symmetric free subalgebra conjecture for division rings with involution
Let be a division ring with center , and let be a -involution on , meaning a -linear map satisfying and for all . An element is symmetric with respect to when .
Makar-Limanov's involutional conjecture. If is infinite dimensional over and finitely generated as a division -algebra, then there exist two symmetric elements in which freely generate a free -subalgebra of .
This is presented as an involutional version of Makar-Limanov's conjecture. The paper describes its results as supporting evidence, so the conjecture remains open in general.
Sources & referencesView supporting material
Primary source
Vitor O. Ferreira, Érica Z. Fornaroli and Jairo Z. Gonçalves, “Free algebras in division rings with an involution”, arXiv:1605.04863 (2016).
Additional references
2 papers in this index state this conjecture (2013–2016). The statement above is taken from the most recent of them; the others are arXiv:1308.6602.
Progress summary
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