Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebras

Gérard Duchamp; Alexander Klyachko; Daniel Krob; Jean-Yves Thibon

doi:10.46298/dmtcs.231

Gérard Duchamp ; Alexander Klyachko ; Daniel Krob ; Jean-Yves Thibon - Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebras

dmtcs:231 - Discrete Mathematics & Theoretical Computer Science, January 1, 1997, Vol. 1 - https://doi.org/10.46298/dmtcs.231

Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebrasArticle

Authors: Gérard Duchamp ¹; Alexander Klyachko ^1,²; Daniel Krob ^3,¹; Jean-Yves Thibon ^4,⁵

1 Laboratoire d'informatique Algorithmique : Fondements et Applications
2 Department of Mathematics [Ankara]
3 Laboratoire Informatique Théorique et Programmation
4 Laboratoire d'informatique Algorithmique : Fondements et Applications
5 Laboratoire d'Informatique Gaspard-Monge

This paper discusses various deformations of free associative algebras and of their convolution algebras. Our main examples are deformations of noncommutative symmetric functions related to families of idempotents in descent algebras, and a simple q-analogue of the shuffle product, which has unexpected connections with quantum groups, hyperplane arrangements, and certain questions in mathematical physics (the quon algebra, generalized Brownian motion).

https://doi.org/10.46298/dmtcs.231

Source: HAL:hal-00018540v2

Volume: Vol. 1

Published on: January 1, 1997

Imported on: March 26, 2015

Keywords: [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA],[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]

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