Differential Calculi on Quantum Spaces Determined by Automorphisms

Abstract

If the bimodule of 1-forms of a differential calculus over an associative algebra is the direct sum of 1-dimensional bimodules, a relation with automorphisms of the algebra shows up. This happens for some familiar quantum space calculi.

Obituary: Aristophanes Dimakis

“…A variety of studies followed, on Noncommutative Geometry [34,35,67], discretization à la Umbral calculus [33], Connes' distance function on discrete sets [42], soliton equations on a "noncommutative space" [52,53,58], Moyal deformation of integrable models [54,56,65,66,68,69,77], automorphisms of real four-dimensional Lie algebras and characterization of four-dimensional homogeneous spaces [62], "functional representations" (generating equations) of integrable hierarchies [72], studies of KP and related hierarchies [75,76,79,80,83,84], relations between different hierarchies via deformation of multiplication [73].…”

Noncommutative Geometries and Gravity

“…• Demanding the existence of a "classical basis" θ i of one-forms: θ i a = a θ i for all a ∈ A [82,86]. In many cases there exists an "almost classical basis": θ i a = φ i (a) θ i with automorphisms φ i of A [87,88].…”