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Non-commutative geometry of finite groups
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
`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?
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
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 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
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
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
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
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