Abstract
Representations of the n-braid group where generators are given by matrices whose elements belong to a noncommutative algebra are discussed. Representation of this algebra in a Hilbert space generalizes the Burau representation. Two algebras which are closely related and are physically indistinguishable provided that a particular eigenvalue is fine tuned are discussed. It is shown that the generalized oscillator system given by one of the algebras generates a hydrogenlike spectrum.
Keywords
Noncommutative geometry
Braid group
Mathematics
Group (periodic table)
Eigenvalues and eigenvectors
Pure mathematics
Spectrum (functional analysis)
Algebra over a field
Representation (politics)
Algebra representation
Hilbert space
Trivial representation
Physics
Quantum mechanics
Subject Areas
Algebraic structures and combinatorial models
·Geometry and Topology ·Physical Sciences
Geometric and Algebraic Topology
·Geometry and Topology ·Physical Sciences
Advanced Algebra and Geometry
·Mathematical Physics ·Physical Sciences
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