A deformation of commutative polynomial algebras in even numbers of variables
Open Mathematics (2010)
- Volume: 8, Issue: 1, page 73-97
- ISSN: 2391-5455
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topWenhua Zhao. "A deformation of commutative polynomial algebras in even numbers of variables." Open Mathematics 8.1 (2010): 73-97. <http://eudml.org/doc/269483>.
@article{WenhuaZhao2010,
abstract = {We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture [8] is reduced to an open problem on this deformation of polynomial algebras.},
author = {Wenhua Zhao},
journal = {Open Mathematics},
keywords = {The generalized Laguerre polynomials; Total symbols of differential operators; The image conjecture; The Jacobian conjecture; the generalized Laguerre polynomials; total symbols of differential operators; the image conjecture; the Jacobian conjecture},
language = {eng},
number = {1},
pages = {73-97},
title = {A deformation of commutative polynomial algebras in even numbers of variables},
url = {http://eudml.org/doc/269483},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Wenhua Zhao
TI - A deformation of commutative polynomial algebras in even numbers of variables
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 73
EP - 97
AB - We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture [8] is reduced to an open problem on this deformation of polynomial algebras.
LA - eng
KW - The generalized Laguerre polynomials; Total symbols of differential operators; The image conjecture; The Jacobian conjecture; the generalized Laguerre polynomials; total symbols of differential operators; the image conjecture; the Jacobian conjecture
UR - http://eudml.org/doc/269483
ER -
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