A braid-like presentation of the integral Steinberg group of type C_2

Autor: Christian Kassel

Publikováno v: Journal of Algebra
Journal of Algebra, Elsevier, 2020, ⟨10.1016/j.jalgebra.2020.09.015⟩

We show that the Steinberg group $\text{St}(C_2,{\mathbb Z})$ associated with the Lie type $C_2$ and with integer coefficients can be realized as a quotient of the braid group $B_6$ by one relation. As an application we give a new braid-like presenta

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https://hal.archives-ouvertes.fr/hal-02880734

The Fourier expansion of $$\varvec{\eta (z)\eta (2z)\eta (3z)/\eta (6z)}$$ η ( z ) η ( 2 z ) η ( 3 z ) / η ( 6 z )

Autor: Christian Kassel, Christophe Reutenauer

Publikováno v: Archiv der Mathematik. 108:453-463

We compute the Fourier coefficients of the weight one modular form \(\eta (z)\eta (2z)\eta (3z)/\eta (6z)\) in terms of the number of representations of an integer as a sum of two squares. We deduce a relation between this modular form and translates

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https://doi.org/10.1007/s00013-017-1033-4

The lazy homology of a Hopf algebra

Autor: Julien Bichon, Christian Kassel

Publikováno v: Journal of Algebra
Journal of Algebra, Elsevier, 2010, 323, pp.2556-2590. ⟨10.1016/j.jalgebra.2009.12.032⟩
Journal of Algebra, 2010, 323, pp.2556-2590. ⟨10.1016/j.jalgebra.2009.12.032⟩

To any Hopf algebra H we associate two commutative Hopf algebras, which we call the first and second lazy homology Hopf algebras of H. These algebras are related to the lazy cohomology groups based on the so-called lazy cocycles of H by universal coe

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Principal fiber bundles in non-commutative geometry

Autor: Christian Kassel

Publikováno v: 9th Summer School on Geometric, Algebraic and Topological Methods for Quantum Field Theory
9th Summer School on Geometric, Algebraic and Topological Methods for Quantum Field Theory, Jul 2015, Villa de Leyva, Colombia. pp.75-133, ⟨10.1007/978-3-319-65427-0_3⟩
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics ISBN: 9783319654263

These are the expanded notes of a course given at the Summer school "Geometric, topological and algebraic methods for quantum field theory" held at Villa de Leyva, Colombia in July 2015. We first give an introduction to non-commutative geometry and t

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https://hal.archives-ouvertes.fr/hal-01937789

Algebraicity of the zeta function associated to a matrix over a free group algebra

Autor: Christian Kassel, Christophe Reutenauer

Publikováno v: Algebra & Number Theory
Algebra & Number Theory, Mathematical Sciences Publishers 2014, pp.8-2 (2014), 497--511. ⟨10.2140/ant.2014.8.497⟩
Algebra Number Theory 8, no. 2 (2014), 497-511

Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic function.