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Publications Influence

Non-commutative geometry of finite groups

- K. Bresser, A. Dimakis, F. Mueller-Hoissen, A. Sitarz
- Mathematics, Physics
- 6 September 1995

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding… Expand

71 8- PDF

Differential calculi and linear connections

- A. Dimakis, J. Madore
- Mathematics
- 23 January 1996

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that… Expand

67 8- PDF

Discrete differential calculus graphs, topologies and gauge theory

- A. Dimakis, F. Muller-Hoissen
- Mathematics, Physics
- 19 April 1994

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a ‘‘reduction’’ of the ‘‘universal… Expand

89 7- PDF

Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

- A. Dimakis, F. Mueller-Hoissen, T. Striker
- Mathematics, Physics
- 21 September 1995

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and… Expand

30 4- PDF

An algebraic scheme associated with the noncommutative KP hierarchy and some of its extensions

- A. Dimakis, Folkert Muller-Hoissen
- Mathematics, Physics
- 2 January 2005

A well-known ansatz ('trace method') for soliton solutions turns the equations of the (non-commutative) KP hierarchy, and those of certain extensions, into families of algebraic sum identities. We… Expand

30 4- PDF

Discrete Riemannian geometry

- A. Dimakis, F. Muller-Hoissen
- Physics, Mathematics
- 8 August 1998

Within a framework of noncommutative geometry, we develop an analog of (pseudo-) Riemannian geometry on finite and discrete sets. On a finite set, there is a counterpart of the continuum metric… Expand

60 4- PDF

Discrete differential manifolds and dynamics on networks

- A. Dimakis, F. Muller-Hoissen, F. Vanderseypen
- Mathematics, Physics
- 21 August 1994

A discrete differential manifold is a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides a convenient… Expand

32 3- PDF

Differential calculus and gauge theory on finite sets

- A. Dimakis, F. Muller-Hoissen
- Mathematics, Physics
- 28 January 1994

We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes'… Expand

52 2- PDF

Matrix KP: tropical limit and Yang–Baxter maps

- A. Dimakis, F. Mueller-Hoissen
- Physics, Mathematics
- 18 August 2017

We study soliton solutions of matrix Kadomtsev–Petviashvili (KP) equations in a tropical limit, in which their support at fixed time is a planar graph and polarizations are attached to its… Expand

13 2- PDF

A Noncommutative version of the nonlinear Schrodinger equation

- A. Dimakis, Folkert Muller-Hoissen
- Physics
- 3 July 2000

We apply a (Moyal) deformation quantization to a bicomplex associated with the classical nonlinear Schrodinger equation. This induces a deformation of the latter equation to noncommutative space-time… Expand

23 2- PDF