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Hochschild and cyclic homology of Yang–Mills algebras
(De Gruyter, 2012-04)
The aim of this article is to present a detailed algebraic computation of the Hochschild and cyclic homology groups of the Yang–Mills algebras YM(n) (n ∈ ℕ≧2) defined by A. Connes and M. Dubois-Violette in [8], continuing ...
Metric geometry of infinite dimensional Lie groups and their homogeneous spaces
(De Gruyter, 2019-09)
We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic ...
On the SO(n + 3) to SO(n) branching multiplicity space Sur l'espace de multiplicité de branchement de SO(n + 3) vers SO(n)
(Elsevier France-editions Scientifiques Medicales Elsevier, 2018-11)
We study the decomposition as an SO(3)-module of the multiplicity space corresponding to the branching from SO(n+3) to SO(n). Here, SO(n) (resp. SO(3)) is considered embedded in SO(n+3) in the upper left-hand block (resp. ...
Level ε
(Université de Picardie Jules Verne, 2019-10)
Lawvere has observed that certain ‘gros’ toposes in algebraic geometry suggest the existence of an ‘infinitesimal level’, closely related to finite-dimensional local algebras. Motivated by this observation we propose an ...
Multiparameter quantum groups, bosonizations and cocycle deformations
(Unión Matemática Argentina, 2017-12)
The multiparameter quantized enveloping algebras Uq(gA) constructed by Pei, Hu and Rosso [Quantum affine algebras, extended affine Lie algebras, and their applications, 145–171, Amer. Math. Soc., Providence, 2010] are ...
On the geometry of generalized inverses
(Wiley VCH Verlag, 2005-04)
We study the set S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of aBanach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A × A. If A is a C∗-algebra, ...