arXiv subjects

Bechir Dali

Publications and source records attributed to Bechir Dali.

3 recordsLinked to original sources

arXiv2014

Note on the cortex of two-step nilpotent Lie algebras

In this paper, we construct an example of a family of $4d$-dimensional two-step nilpotent Lie algebras $(\frak g_d)_{d\geq 2}$ so that the cortex of the dual of each $\frak g_d$ is a projective algebraic set. More precisely, we show that the cortex of each dual $\frak g_d^*$ of $\frak g_d$ is the zero set of a homogeneous polynomial of degree $d$. This example is a generalization of one given in "Irreducible representations of locally compact groups that cannot be Hausdorff separated from the identity representation" by "{\sc M.E.B. Bekka, and E. Kaniuth}".

math.RT↗

arXiv2009

The spaces $\mathrm{H}^n(\mathfrak{osp}(1|2),M)$ for some weight modules $M$

We entirely compute the cohomology for a natural and large class of $\mathfrak{osp}(1|2)$ modules $M$. We study the restriction to the $\mathfrak{sl}(2)$ cohomology of $M$ and apply our results to the module $M={\mathfrak D}_{λ,μ}$ of differential operators on the super circle, acting on densities.

math.QA↗

arXiv2008

Linear family of Lie brackets on the space of matrices $Mat(n\times m,\K)$ and Ado's Theorem

In this paper we classify a linear family of Lie brackets on the space of rectangular matrices $Mat(n\times m,\K)$ and we give an analogue of the Ado's Theorem. We give also a similar classification on the algebra of the square matrices $Mat(n, \K)$ and as a consequence, we prove that we can't built a faithful representation of the $(2n+1)$-dimensional Heisenberg Lie algebra $\mathfrak{H}_n$ in a vector space $V$ with $\dim V\leq n+1$. Finally, we prove that in the case of the algebra of square matrices $Mat(n,\K)$, the corresponding Lie algebras structures are a contraction of the canonical Lie algebra $\mathfrak{gl}(n,\K)$.

math.RT↗