Noncommutative Deformations of Thick Points

Journal of Singularities
volume 18 (2018), 427-439

Received: 30 December 2017. Accepted: 23 January 2018.

DOI: 10.5427/jsing.2018.18v

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Abstract:

Any commutative algebra is of course also an associative algebra, and we may deform it as a non-commutative associative algebra. In particular this is of interest in singularity theory. It turns out that the versal base space of the non-commutative deformation functor of a thick point, in an affine three-dimensional variety, has properties that are rather astonishing. This base space is the main ingredient of a Toy Model for Quantum Theory, published in several books and papers. In this paper I shall describe the problems related to the computation of the local moduli suite of the singularity consisting of an isolated point with a 3-dimensional tangent space.

Author(s) information:

Olav Arnfinn Laudal
Matematisk institutt
University of Oslo
Pb. 1053, Blindern
N-0316 Oslo, Norway
email: arnfinnl@math.uio.no