Gérard Duchamp ; Alexander Klyachko ; Daniel Krob ; Jean-Yves Thibon
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Noncommutative symmetric functions III : Deformations of Cauchy and convolution algebras
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).
Anh Trong Nam Hoang, 2024, Fox–Neuwirth cells, quantum shuffle algebras, and the homology of type-B Artin groups, Mathematische Zeitschrift, 306, 4, 10.1007/s00209-024-03445-4.
Milena Sošić, 2024, The inverse of a quantum bilinear form of the oriented braid arrangement, Hrčak Portal of scientific journals of Croatia (University Computing Centre), 59, 1, pp. 51-75, 10.3336/gm.59.1.03, https://hrcak.srce.hr/318150.
Florent Hivert;Jean-Christophe Novelli;Jean-Yves Thibon, 2005, Yang–Baxter bases of 0-Hecke algebras and representation theory of 0-Ariki–Koike–Shoji algebras, Advances in Mathematics, 205, 2, pp. 504-548, 10.1016/j.aim.2005.07.016, https://doi.org/10.1016/j.aim.2005.07.016.
Michiel Hazewinkel, 2005, Symmetric Functions, Noncommutative Symmetric Functions and Quasisymmetric Functions II, Acta Applicandae Mathematicae, 85, 1-3, pp. 319-340, 10.1007/s10440-004-5635-z.