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Jacques Dixmier and Nguyen Huu Anh Conjectures on the Weil Algebra A1(K).

Man Nguyen Van Minh

出版	SSRN, 2018
URL	http://books.google.com.hk/books?id=p136zgEACAAJ&hl=&source=gbs_api

註釋

Recall that the is a non-commutative algebra over a field k with two generators x and y satisfying Lie relation [x,y]=xy-yx = 1. In 1968 Jacques Dixmier stated a conjecture as follows: Every non zero homomorphism from A(k)into itself is an isomorphism. Until now, it is not known that Dixmier's conjecture is true or not. Therefore, in 1990, Professor Nguyen Huu Anh try to find a counter example for that statement in some special cases. To support this efforts, he used some new techniques (Groebner bases method) and exploiting a powerful symbolic computing system, Maple. After getting some preliminary results, Prof. Anh propose the following conjecture: Let P and Q be two polynomials of degrees p,q (p ≥ 1 or q ≥ 1) in the Weyl algebra A(k) = k[x,y], k is algebraically closed field. Assume that: + gcd(p,q)