Noncommutative Geometry of the h-deformed Quantum Plane
نویسنده
چکیده
The h-deformed quantum plane is a counterpart of the q-deformed one in the set of quantum planes which are covariant under those quantum deformations of GL(2) which admit a central determinant. We have investigated the noncommutative geometry of the h-deformed quantum plane. There is a 2-parameter family of torsion-free linear connections, a 1-parameter sub-family of which are compatible with a skew-symmetric non-degenerate bilinear map. The skew-symmetric map resembles a symplectic 2-form and induces a metric. It is also shown that the extended h-deformed quantum plane is a noncommutative version of the Poincaré half-plane, a surface of constant negative Gaussian curvature. Semyung Preprint SMHEP 97/8 ∗Laboratoire associé au CNRS, URA D0063
منابع مشابه
Automorphisms of associative algebras and noncommutative geometry
A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the h-deformed plane and the quantum group GLp,q(2) are recovered in this way. Geometric structures like metrics and compatible linear connections are introduced.
متن کاملStability of additive functional equation on discrete quantum semigroups
We construct a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...
متن کاملNoncommutative Conformal Field Theory in the Twist - deformed context
We discuss conformal symmetry on the two dimensional noncommutative plane equipped with Moyal product in the twist deformed context. We show that the consistent use of the twist procedure leads to results which are free from ambiguities. This lends support to the importance of the use of twist symmetries in noncommutative geometry.
متن کاملNoncommutative Rigidity
Using very weak criteria for what may constitute a noncommutative geometry, I show that a pseudo-Riemannian manifold can only be smoothly deformed into noncommutative geometries if certain geometric obstructions vanish. These obstructions can be expressed as a system of partial differential equations relating the metric and the Poisson structure that describes the noncommutativity. I illustrate...
متن کاملGeometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
A detailed description of the infinite-dimensional Lie algebra of ⋆-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C∗-algebra of compact o...
متن کامل