publication . Preprint . 2014

Inhomogeneous linear equation in Rota-Baxter algebra

Pietrzkowski, Gabriel;
Open Access English
  • Published: 09 May 2014
Abstract
We consider a complete filtered Rota-Baxter algebra of weight $\lambda$ over a commutative ring. Finding the unique solution of a non-homogeneous linear algebraic equation in this algebra, we generalize Spitzer's identity in both commutative and non-commutative cases. As an application, considering the Rota-Baxter algebra of power series in one variable with q-integral as the Rota-Baxter operator, we show certain Eulerian identities.
Subjects
arXiv: Mathematics::CombinatoricsMathematics::Commutative AlgebraMathematics::Quantum AlgebraNonlinear Sciences::Exactly Solvable and Integrable Systems
free text keywords: Mathematics - Rings and Algebras, 13P99, 16W99, 16Z05
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