145 citations · 907 across the 49 of their papers we have counts for
27 papers · 1 filter
Clifford algebras, meson algebras and higher order generalisations
Michel Dubois-Violette, Blas Torrecillas
We analyse the homogeneous parts of Clifford and meson algebras and point out that for the Clifford algebra it is related to fermionic statistics, that is, to fermionic parastatist…
Quadratic differential algebras generated by Euclidean spaces
Michel Dubois-Violette, Giovanni Landi
We define a class of quadratic differential algebras which are generated as differential graded algebras by the elements of an Euclidean space. Such a differential algebra is a dif…
Principal fibrations over noncommutative spheres
Michel Dubois-Violette, Xiao Han, Giovanni Landi
We present examples of noncommutative four-spheres that are base spaces of -principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinat…
Differential calculus on Jordan algebra and Jordan modules
Alessandro Carotenuto, Ludwik Dabrowski, Michel Dubois-Violette
Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on…
Noncommutative Euclidean spaces
Michel Dubois-Violette, Giovanni Landi
We give a definition of noncommutative finite-dimensional Euclidean spaces . We then remind our definition of noncommutative products of Euclidean spaces $\mathbb R^{N…
Noncommutative products of Euclidean spaces
Michel Dubois-Violette, Giovanni Landi
We present natural families of coordinate algebras of noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an R-matrix which is…
Exceptional quantum geometry and particle physics
Michel Dubois-Violette
Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group and on the existence of 3 generations, we develop an argumentation…
The quantum group of a preregular multilinear form
Julien Bichon, Michel Dubois-Violette
We describe the universal quantum group preserving a preregular multilinear form, by means of an explicit finite presentation of the corresponding Hopf algebra.
Poincaré duality for Koszul algebras
Michel Dubois-Violette
We discuss the consequences of the Poincaré duality, versus AS- Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poi…
Half-commutative orthogonal Hopf algebras
Julien Bichon, Michel Dubois-Violette
A half-commutative orthogonal Hopf algebra is a Hopf *-algebra generated by the self-adjoint coefficients of an orthogonal matrix corepresentation that half commute in…
Young tableaux and homotopy commutative algebras
Michel Dubois-Violette, Todor Popov
A homotopy commutative algebra, or -algebra, is defined via the Tornike Kadeishvili homotopy transfer theorem on the vector space generated by the set of Young tableaux…
The Weil Algebra of a Hopf Algebra - I - A noncommutative framework
Michel Dubois-Violette, Giovanni Landi
We generalize the notion, introduced by Henri Cartan, of an operation of a Lie algebra in a graded differential algebra . We define the notion of an operation of a…
From Koszul duality to Poincaré duality
Michel Dubois-Violette
We discuss the notion of Poincaré duality for graded algebras and its connections with the Koszul duality for quadratic Koszul algebras. The relevance of the Poincaré duality is po…
Lie prealgebras
Michel Dubois-Violette, Giovanni Landi
We introduce a generalization of Lie algebras within the theory of nonhomogeneous quadratic algebras and point out its relevance in the theory of quantum groups. In particular the…
Tensor product of N-complexes and generalization of graded differential algebras
Michel Dubois-Violette
It is known that the notion of graded differential algebra coincides with the notion of monoid in the monoidal category of complexes. By using the monoidal structure introduced by…
Noncommutative coordinate algebras
Michel Dubois-Violette
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (non…
Multilinear forms and graded algebras
Michel Dubois-Violette
In this paper we investigate the class of the connected graded algebras which are finitely generated in degree 1, which are finitely presented with relations of degrees greater or…
Inhomogeneous Yang-Mills algebras
Roland Berger, Michel Dubois-Violette
We determine all inhomogeneous Yang-Mills algebras and super Yang-Mills algebras which are Koszul. Following a recent proposal, a non-homogeneous algebra is said to be Koszul if th…
Non commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres
Alain Connes, Michel Dubois-Violette
This paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic…
Homogeneous algebras, statistics and combinatorics
Michel Dubois-Violette, Todor Popov
After some generalities on homogeneous algebras, we give a formula connecting the Poincaré series of a homogeneous algebra with the homology of the corresponding Koszul complex gen…
Yang-Mills algebra
Alain Connes, Michel Dubois-Violette
Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang-Mills connection over the (s+1)-dimensional pseudo Euclidean space are poin…
Homogeneous algebras
Roland Berger, Michel Dubois-Violette, Marc Wambst
Various concepts associated with quadratic algebras admit natural generalizations when the quadratic algebras are replaced by graded algebras which are finitely generated in degree…
Tensor fields of mixed Young symmetry type and N-complexes
Michel Dubois-Violette, Marc Henneaux
We construct -complexes of non completely antisymmetric irreducible tensor fields on which generalize the usual complex of differential forms. Although, fo…
Smooth *-algebras
Michel Dubois-Violette, Andreas Kriegl, Yoshiaki Maeda +1
Looking for the universal covering of the smooth non-commutative torus leads to a curve of associative multiplications on the space $\Cal O_M'(\Bbb R^{2n})\cong \Cal O_C(\Bbb R^{2n…