Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A noncommutative geometric analysis of a sphere-torus topology change
AU - Gratus, J
PY - 2004/2
Y1 - 2004/2
N2 - A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or variety. The topology of the manifold or variety depends on the parameter, varying from nothing, to a point, a sphere, a certain variety and finally a torus. The irreducible adjoint preserving representations of the noncommutative algebras are studied. As well as typical noncommutative sphere type representations and noncommutative torus type representations, a new object is discovered and called a sphere-torus.
AB - A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or variety. The topology of the manifold or variety depends on the parameter, varying from nothing, to a point, a sphere, a certain variety and finally a torus. The irreducible adjoint preserving representations of the noncommutative algebras are studied. As well as typical noncommutative sphere type representations and noncommutative torus type representations, a new object is discovered and called a sphere-torus.
KW - noncommutative geometry
KW - deformation quantisation
KW - sphere torus
KW - topology change
U2 - 10.1016/S0393-0440(03)00072-X
DO - 10.1016/S0393-0440(03)00072-X
M3 - Journal article
VL - 49
SP - 156
EP - 175
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
SN - 0393-0440
IS - 2
ER -