Bernoulli-type relations in some noncommutative polynomial ring

Murata, Shunsuke

Tsukuba J. Math., Tome 34 (2010) no. 1, p. 97-116 / Harvested from Project Euclid

Résumé

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.

Publié le : 2010-08-15
Classification: Polynomial ring, Bernoulli number, Representation, Enveloping algebra, 17B35, 11R09

@article{1283967410,
     author = {Murata, Shunsuke},
     title = {Bernoulli-type relations in some noncommutative polynomial ring},
     journal = {Tsukuba J. Math.},
     volume = {34},
     number = {1},
     year = {2010},
     pages = { 97-116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1283967410}
}

Murata, Shunsuke. Bernoulli-type relations in some noncommutative polynomial ring. Tsukuba J. Math., Tome 34 (2010) no. 1, pp.  97-116. http://gdmltest.u-ga.fr/item/1283967410/