arXiv subjects

M. Dubois-Violette

Publications and source records attributed to M. Dubois-Violette.

4 recordsLinked to original sources

arXiv1999

A Finite Dimensional Gauge Problem in the WZNW Model

The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each of these matrix algebras admits an ideal such that the corresponding factor algebra is finite dimensional. The structure of superselection sectors of the (diagonal) 2D WZNW model is then reduced to a finite dimensional problem of a gauge theory type. For n=2 this problem is solved using a generalized BRS formalism.

hep-th↗

arXiv1995

On Curvature in Noncommutative Geometry

A general definition of a bimodule connection in noncommutative geometry has been recently proposed. For a given algebra this definition is compared with the ordinary definition of a connection on a left module over the associated enveloping algebra. The corresponding curvatures are also compared.

q-alg↗

arXiv1994

A common generalization of the Frölicher-Nijenhuis bracket and the Schouten bracket for symmetry multi vector fields

There is a canonical mapping from the space of sections of the bundle $\wedge T^\ast M\otimes ST\ M$ to $Ω(T^\ast M ; T(T^\ast M))$. It is shown that this is a homomorphism on $Ω(M;TM) for the Frölicher-Nijenhuis brackets, and also on $Γ(ST\ M)$ for the Schouten bracket of symmetric multi vector fields. But the whole image is not a subalgebra for the Frölicher-Nijenhuis bracket on $Ω(T^\ast M;T(T^\ast M))$.

alg-geom↗

arXiv1992

General Solution of the Consistency Equation

We produce the general solution of the Wess-Zumino consistency condition for gauge theories of the Yang-mills type, for any ghost number and form degree. We resolve the problem of the cohomological independence of these solutions. In other words we fully describe the local version of the cohomology of the BRS operator, modulo the differential on space--time. This in particular includes the presence of external fields and non--trivial topologies of space--time.

hep-th↗