JournalsowrVol. 10, No. 3pp. 2501–2552

Matrix Factorizations in Algebra, Geometry, and Physics

  • Ragnar-Olaf Buchweitz

    University of Toronto at Scarborough, Canada
  • Kentaro Hori

    The University of Tokyo, Kashiwa, Japan
  • Henning Krause

    Universität Bielefeld, Germany
  • Christoph Schweigert

    Universität Hamburg, Germany
Matrix Factorizations in Algebra, Geometry, and Physics cover
Download PDF

A subscription is required to access this article.

Abstract

Let WW be a polynomial or power series in several variables, or, more generally, a nonzero element in some regular commutative ring. A matrix factorization of WW consists of a pair of square matrices XX and YY of the same size, with entries in the given ring, such that the matrix product XYXY is WW multiplied by the identity matrix. For example, if XX is a matrix whose determinant is WW and YY is its adjoint matrix, then (X,Y)(X, Y) is a matrix factorization of WW.

Such matrix factorizations are nowadays ubiquitous in several different fields in physics and mathematics, including String Theory, Commutative Algebra, Algebraic Geometry, both in its classical and its noncommutative version, Singularity Theory, Representation Theory, Topology, there in particular in Knot Theory.

The workshop has brought together leading researchers and young colleagues from the various input fields; it was the first workshop on this topic in Oberwolfach. For some leading researchers from neighboring fields, this was their first visit to Oberwolfach.

Cite this article

Ragnar-Olaf Buchweitz, Kentaro Hori, Henning Krause, Christoph Schweigert, Matrix Factorizations in Algebra, Geometry, and Physics. Oberwolfach Rep. 10 (2013), no. 3, pp. 2501–2552

DOI 10.4171/OWR/2013/44