Bernoulli-type Relations in Some Noncommutative Polynomial Ring

Details Bernoulli-type Relations in Some Noncommutative Polynomial Ring Bernoulli-type Relations in Some Noncommutative Polynomial Ring

2009-12-09

arxiv.org/abs/0912.1711v1

Mathematics

Rings and Algebras

19 pages

Scientific paper

We find particular relations which we call "Bernoulli-type" in some noncommutative polynomial ring with a single nontrivial relation. More precisely, our ring is isomorphic to the universal enveloping algebra of a two-dimensional non-abelian Lie algebra. From these Bernoulli-type relations in our ring, we can obtain a representation on a certain left ideal with the Bernoulli numbers as structure constants.

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