The Dixmier conjecture and the shape of possible counterexamples

Details The Dixmier conjecture and the shape of possible counterexamples The Dixmier conjecture and the shape of possible counterexamples

2011-11-25

arxiv.org/abs/1111.6100v1

Mathematics

Rings and Algebras

40 pages; 11 figures

Scientific paper

We introduce the notion of an irreducible pair of elements in the first Weyl algebra W. Then we show that each endomorphism of W which is not an automorphism, can be transformed into one that applies the canonical generators of W onto an irreducible pair with a specific shape (subrectangular). Consequently, the Dixmier conjecture is true if and only if there are no such irreducible pairs.

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