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Local derivations for quotient and factor algebras of polynomials

Andrzej Nowicki, Ilona Nowosad (2003)

Colloquium Mathematicae

We describe all Kadison algebras of the form S - 1 k [ t ] , where k is an algebraically closed field and S is a multiplicative subset of k[t]. We also describe all Kadison algebras of the form k[t]/I, where k is a field of characteristic zero.

Matrix factorizations for domestic triangle singularities

Dawid Edmund Kędzierski, Helmut Lenzing, Hagen Meltzer (2015)

Colloquium Mathematicae

Working over an algebraically closed field k of any characteristic, we determine the matrix factorizations for the-suitably graded-triangle singularities f = x a + y b + z c of domestic type, that is, we assume that (a,b,c) are integers at least two satisfying 1/a + 1/b + 1/c > 1. Using work by Kussin-Lenzing-Meltzer, this is achieved by determining projective covers in the Frobenius category of vector bundles on the weighted projective line of weight type (a,b,c). Equivalently, in a representation-theoretic context,...

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