An analogue of the Conjecture of Dixmier is true for the algebra of polynomial integro-differential operators

作者：Bavula V V^*

来源：Journal of Algebra, 2012, 372: 237-250.

DOI：10.1016/j.jalgebra.2012.09.009

• The Weyl algebra
• The Conjecture/Problem of Dixmier
• The algebra of polynomial integro-differential operators
• The Jacobian Conjecture

Let A(1) := K %26lt; x, d/dx) be the Weyl algebra and I-1 := K %26lt; x, d/dx, integral %26gt; be the algebra of polynomial integro-differential operators over a field K of characteristic zero. The Conjecture/Problem of Dixmier (1968) [still open]: is an algebra endomorphism of the Weyl algebra A(1) an automorphism? The aim of the paper is to prove that each algebra endomorphism of the algebra I-1 is an automorphism. Notice that in contrast to the Weyl algebra A(1) the algebra I-1 is a non-simple, non-Noetherian algebra which is not a domain. Moreover, it contains infinite direct sums of nonzero left and right ideals.

• 出版日期2012-12-15