Toukaiddine Petit

activity

20042025

most citedOn the Generalized Enveloping Algebra of a Color Lie Algebra

1 citations · 1 across the 8 of their papers we have counts for

collaborators

8 papers

math.RA2025

On Graded Deformations of The universal Enveloping Algebra of a Color Lie Algebra

Toukaiddine Petit

Let $g$ be a Color Lie Algebra and $U (g)$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit gra…

math.RA2024

Index a Lie Borel Lie Algebra

Toukaiddine Petit

We compute the index of a Lie Borel Lie Algbra of a simple Lie algebra.

math.RA2010

Versal Deformations and Versality in Central Extensions of Jacobi's Schemes

Roger Carles, Toukaiddine Petit

Let $Ł_{m}$ be the scheme of the laws defined by the Jacobi's identities on $\K^m$ with $\K$ a field. A deformation of $\g\inŁ_m$, parametrized by a local $\K$-algebra $\A$, is a loc…

math.AG2007

Deformations of Lie algebras and Induction of Schemes

Roger Carles, Toukaiddine Petit

Let $Ł_{m}$ be the scheme of the laws defined by the identities of Jacobi on $\K^m$. The local studies of an algebraic Lie algebra $\g=\mathrm{R}\ltimes\n$ in $Ł_{m}$ and its nilpotent…

math.RA2005★ 1 cited

On the Generalized Enveloping Algebra of a Color Lie Algebra

Toukaiddine Petit, Freddy Van Oystaeyen

Let $G$ be an abelien group, $ε$ an anti-bicharacter of $G$ and $L$ a $G$ -graded $ε$ Lie algebra (color Lie algebra) over $\K$ a field of characteristic zero. We prove that all $G$ …

math-ph2005

Note on The Cohomology of Color Hopf and Lie Algebras

Xiao-Wu Chen, Toukaiddine Petit, Freddy Van Oystaeyen

Let $A$ be a $(G, χ)$ -Hopf algebra with bijection antipode and let $M$ be a $G$ -graded $A$ -bimodule. We prove that there exists an isomorphism \mathrm{HH}^*_{\rm gr}(A, M)\cong{\rm…