Degree estimate for subalgebras generated by two elements

Leonid Makar-Limanov; Jie-Tai Yu

Journal of the European Mathematical Society (2008)

  • Volume: 010, Issue: 2, page 533-541
  • ISSN: 1435-9855

Abstract

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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, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.

How to cite

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Makar-Limanov, Leonid, and Yu, Jie-Tai. "Degree estimate for subalgebras generated by two elements." Journal of the European Mathematical Society 010.2 (2008): 533-541. <http://eudml.org/doc/277201>.

@article{Makar2008,
abstract = {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, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.},
author = {Makar-Limanov, Leonid, Yu, Jie-Tai},
journal = {Journal of the European Mathematical Society},
keywords = {degree estimate; two-generated subalgebras; polynomial algebras; free associative algebras; commmutators; Jacobians; lemma on radicals; degree estimates; two-generator subalgebras; commutators; Jacobians; tame automorphism},
language = {eng},
number = {2},
pages = {533-541},
publisher = {European Mathematical Society Publishing House},
title = {Degree estimate for subalgebras generated by two elements},
url = {http://eudml.org/doc/277201},
volume = {010},
year = {2008},
}

TY - JOUR
AU - Makar-Limanov, Leonid
AU - Yu, Jie-Tai
TI - Degree estimate for subalgebras generated by two elements
JO - Journal of the European Mathematical Society
PY - 2008
PB - European Mathematical Society Publishing House
VL - 010
IS - 2
SP - 533
EP - 541
AB - 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, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.
LA - eng
KW - degree estimate; two-generated subalgebras; polynomial algebras; free associative algebras; commmutators; Jacobians; lemma on radicals; degree estimates; two-generator subalgebras; commutators; Jacobians; tame automorphism
UR - http://eudml.org/doc/277201
ER -

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