Geodesic
Degree estimate for subalgebras generated by two elements
Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 533-541

Voir la notice de l'article provenant de la source EMS Press

We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, that plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.
DOI : 10.4171/jems/121
Classification : 13-XX, 14-XX, 16-XX, 00-XX
Keywords: Degree estimate, two-generated subalgebras, polynomial algebras, free associative algebras, commmutators, Jacobians 
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     author = {Leonid Makar-Limanov and Jie-Tai Yu},
     title = {Degree estimate for subalgebras generated by two elements},
     journal = {Journal of the European Mathematical Society},
     pages = {533--541},
     publisher = {mathdoc},
     volume = {10},
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     year = {2008},
     doi = {10.4171/jems/121},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/121/}
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Leonid Makar-Limanov; Jie-Tai Yu. Degree estimate for subalgebras generated by two elements. Journal of the European Mathematical Society, Tome 10 (2008) no. 2, pp. 533-541. doi: 10.4171/jems/121

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