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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

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

Teleparallelism-A viable theory of gravity?

- F. Mueller-Hoissen, J. Nitsch
- Physics
- 15 August 1983

The teleparallelism theory of gravity is presented as a constrained Poincare gauge theory. Arguments are given in favor of a two-parameter family of field Lagrangians quadratic in torsion. The… Expand

KP line solitons and Tamari lattices

- A. Dimakis, F. Mueller-Hoissen
- Mathematics, Physics
- 9 September 2010

The KP-II equation possesses a class of line soliton solutions which can be qualitatively described via a tropical approximation as a chain of rooted binary trees, except at "critical" events where a… Expand

Integrable Discretizations of Chiral Models

- A. Dimakis, F. Mueller-Hoissen
- Mathematics, Physics
- 3 December 1995

A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises… Expand

Bidifferential calculus approach to AKNS hierarchies and their solutions

- A. Dimakis, F. Mueller-Hoissen
- Physics, Mathematics
- 9 April 2010

We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quickly… Expand

KP Solitons, Higher Bruhat and Tamari Orders

- A. Dimakis, F. Mueller-Hoissen
- Mathematics, Physics
- 16 October 2011

In a tropical approximation, any tree-shaped line soliton solution, a member of the simplest class of soliton solutions of the Kadomtsev-Petviashvili (KP-II) equation, determines a chain of planar… Expand

KdV soliton interactions: a tropical view

- A. Dimakis, F. Mueller-Hoissen
- Mathematics, Physics
- 7 August 2013

Via a tropical limit (Maslov dequantization), Korteweg-deVries (KdV) solitons correspond to piecewise linear graphs in two-dimensional space-time. We explore this limit.

SOLITON EQUATIONS AND THE ZERO CURVATURE CONDITION IN NONCOMMUTATIVE GEOMETRY

- A. Dimakis, F. Mueller-Hoissen
- Mathematics, Physics
- 1 August 1996

Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for connections with noncommutative differential calculi. The Burgers equation is formulated in this way and… Expand

Noncommutative differential calculus, gauge theory and gravitation

- A. Dimakis, F. Mueller-Hoissen
- Physics
- 1992

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