Deformations of modules of differential forms

B. Agrebaoui; M. Ben Ammar; N. Ben Fraj; V. Ovsienko

doi:10.2991/jnmp.2003.10.2.3

Home/Archive/arXiv

arXiv · math/0310494

Deformations of modules of differential forms

B. Agrebaoui·M. Ben Ammar·N. Ben Fraj·V. Ovsienko

View original source ↗Read source document ↗Export metadata ↓

Abstract

We study non-trivial deformations of the natural action of the Lie algebra $\mathrm{Vect}({\mathbb R}^n)$ on the space of differential forms on ${\mathbb R}^n$. We calculate abstractions for integrability of infinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation in the sense of \cite{ff}.

Explore related subjects

math.QA

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

B. Agrebaoui, M. Ben Ammar, N. Ben Fraj, V. Ovsienko. 2003-10-31. Deformations of modules of differential forms. https://doi.org/10.2991/jnmp.2003.10.2.3

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Maximality Levels of the classical permutation group in the quantum permutation group

Progress on the conjecture of Banica and Bichon that the classical permutation group is a maximal quantum subgroup of the quantum permutation group remains limited to a handful of small-parameter results. By Tannaka--Krein duality, any counterexample to this Maximality Conjecture must arise from a category strictly intermediate between the category $\mathcal{NC}$ of non-crossing partitions and the category $\mathcal{P}$ of all partitions. Any such exotic category must therefore contain a linear combination of crossing-partition vectors. The categories generated by $\mathcal{NC}$ together with some such vectors are studied, with a number of generation results. It is shown that no exotic category can contain a linear combination of three crossing-partition vectors, and, using an argument of ChatGPT to account for a five-dimensional gap, there is no exotic category distinguished from $\mathcal{NC}$ or $\mathcal{P}$ at moments of order six.

math.QA↗

arXiv2026

Pre-modular fusion categories of global dimension $2p$

Let $p>5$ be a prime. In this paper, we show that a pre-modular fusion category of global dimension $2p$ is either pointed or tensor equivalent to $\text{Rep}(D_{2p})$.

math.QA↗

arXiv2026

Graded Automorphism of Multiparameter Quantum Matrix Algebra

We determine the graded automorphism group of the multiparameter quantum matrix algebra $\mathcal O_{λ,\mathbf p}(M_n(\Bbbk))$ over an arbitrary field $\Bbbk$ for all $n\ge2$ and $λ\ne1$. No other restrictions are assumed on $\mathbf p$ or $λ$. Every graded automorphism is a torus automorphism, possibly followed by transposition or by simultaneous reversal of the row and column indices. We give the precise parameter conditions for these two involutions. As an application, we also determine the full automorphism group when the multiplicative group generated by the parameters is torsion-free.

math.QA↗