publication . Preprint . 2014

Inhomogeneous linear equation in Rota-Baxter algebra

Pietrzkowski, Gabriel;
Open Access English
  • Published: 09 May 2014
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.
arXiv: Mathematics::CombinatoricsMathematics::Commutative AlgebraMathematics::Quantum AlgebraNonlinear Sciences::Exactly Solvable and Integrable Systems
free text keywords: Mathematics - Rings and Algebras, 13P99, 16W99, 16Z05
Download from

eλu − 1 eP (u)P e−P (u)a0 (27) P − X = (1 − t) Y [6] Ebrahimi-Fard, K., Guo, L., and Kreimer, D. Integrable renormalization II: the general case. In Annales Henri Poincare (2005), vol. 6, Springer, pp. 369-395.

[7] Ebrahimi-Fard, K., Guo, L., and Manchon, D. Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion. Communications in mathematical physics 267, 3 (2006), 821-845.

[8] Ebrahimi-Fard, K., and Manchon, D. A Magnus-and Fer-type formula in dendriform algebras. Foundations of Computational Mathematics 9, 3 (2009), 295-316.

[9] Guo, L. An Introduction to Rota-Baxter Algebra, vol. 2. International Press, 2012.

[10] Kingman, J. Spitzer's identity and its use in probability theory. Journal of the London Mathematical Society 1, 1 (1962), 309-316.

[11] Magnus, W. On the exponential solution of differential equations for a linear operator. Communications on pure and applied mathematics 7, 4 (1954), 649-673. [OpenAIRE]

[12] Rota, G.-C. Baxter operators, an introduction, Kung JPS, Gian-Carlo Rota on Combinatorics, Introductory Papers and Commentaries, 1995.

[13] Rota, G.-C. Baxter algebras and combinatorial identities. I. Bulletin of the American Mathematical Society 75, 2 (1969), 325-329. [OpenAIRE]

[14] Rota, G.-C. Baxter algebras and combinatorial identities. II. Bulletin of the American Mathematical Society 75, 2 (1969), 330-334. [OpenAIRE]

[15] Rota, G.-C., and Smith, D. Fluctuation theory and Baxter algebras. In Symposia Mathematica (1972), vol. 9, pp. 179- 201.

[16] Spitzer, F. A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc 82, 2 (1956), 323-339. [OpenAIRE]

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue