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  1. Home > Articles & Issues >
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  3. Noncommutative symme ...
Article

Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebras

Gérard Duchamp (1), Alexander Klyachko (1) (2), Daniel Krob (3) (1), Jean-Yves Thibon ORCID (1) (4)
(1) Laboratoire d'informatique Algorithmique : Fondements et Applications
(2) Department of Mathematics [Ankara]
(3) Laboratoire Informatique Théorique et Programmation
(4) Laboratoire d'Informatique Gaspard-Monge
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March 26, 2015
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January 1, 1997
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Volume 1
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10.46298/dmtcs.231
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Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebras

Gérard Duchamp (1), Alexander Klyachko (1) (2), Daniel Krob (3) (1), Jean-Yves Thibon ORCID (1) (4)
(1) Laboratoire d'informatique Algorithmique : Fondements et Applications
(2) Department of Mathematics [Ankara]
(3) Laboratoire Informatique Théorique et Programmation
(4) Laboratoire d'Informatique Gaspard-Monge
Abstract
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).
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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