arXiv subjects

Hedi Regeiba

Publications and source records attributed to Hedi Regeiba.

5 recordsLinked to original sources

arXiv2025

On the free commutative monoid over a positive operad

We study algebraic structures on the free commutative twisted algebra generated by a positive operad $\mathbf q$, in the framework of vector species. Given a nonunital commutative twisted algebra structure $μ$ on $\mathbf q$, we introduce the notion of $μ$-compatible operad structure, leading to a nonunital operad structure on $\mathbf E \circ \mathbf q$, where $\mathbf E$ stands for the exponential species. Next, we define nested pre-Lie operads (NPL-operads), a weak form of the notion of operad, in which the nested associativity axiom is weakened down to a nested pre-Lie condition. This structure is new up to our knowledge. Several constructions of NPL-operads are presented. Finally, we define algebras over a NPL-operad, based on the notion of polynomial functions.

math.CO↗

arXiv2021

The C*-algebra of the variable Mautner group

Let $\M=P\times{M}$ be a variable Mautner group. We describe the $C^*$-algebra $C^*(\M)$ of $\M$ in terms of an algebra of operator fields defined over $P\times{\C^2} $.

math.OA↗

arXiv2019

The C*-algebra of the semi-direct product K and A

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of $G $, generalizing previous results obtained for some special classes of such groups.

math.OA↗

arXiv2019

The $C^*$-algebra of the Cartan motion groups

Let $G_0=K\ltimes\p$ be the Cartan motion groups. Under some assumption on $G_0,$ we describe the $C^*$-algebra $C^*(G_0)$ of $G_0$ in terms of operator fields.

math.GR↗

arXiv2013

C*-algebras with norm controlled dual limits and nilpotent Lie groups

Motivated by the description of the C*-algebras of 5 dimensional nilpotent Lie groups as algebras of operator fields defined over their spectra, we introduce the family of C* -algebras with norm controlled dual limits and we show that the C* -algebras of the 5 dimensional nilpotents Lie groups belong to this class.

math.GR↗