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Tensor products of matrix factorizations

Published online by Cambridge University Press:  22 January 2016

Yuji Yoshino
Yuji Yoshino*
Affiliation:
Institute of Math., Faculty of Integrated Human Studies, Kyoto Univ., Yoshida-Nihonmatsu, Sakyo-ku, Kyoto 606-01, Japan, yoshinoQmath.h.kyoto-u.ac.jp
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Abstract.

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Let K be a field and let f ∈ K[[x1, x2,…,xr]] and g ∈ K[[y1, y2,…,ys]] be non-zero and non-invertible elements. If X (resp. Y) is a matrix factorization of f (resp. g), then we can construct the matrix factorization X ⊗̂ Y of f + g over K[[x1, x2,…,xr, y1, y2,…,ys]], which we call the tensor product of X and Y.

After showing several general properties of tensor products, we will prove theorems which give bounds for the number of indecomposable components in the direct decomposition of X ⊗̂ Y.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 152 , December 1998 , pp. 39 - 56
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

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