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**1 - 8**of**8**### SIMPLE-MINDED SYSTEMS, CONFIGURATIONS AND MUTATIONS FOR REPRESENTATION-FINITE SELF-INJECTIVE ALGEBRAS

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"... Abstract. In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the fir ..."

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Abstract. In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second

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, 2002

"... This project offers an overview of the use of Cellular Automata (CA) as a statistical technique to study complex systems. First, elementary CA, such as the ones studied by Wolfram, will be presented in detail. Then, the role of CA as a tool to study statistical mechanics systems will be demonstrated ..."

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This project offers an overview of the use of Cellular Automata (CA) as a statistical technique to study complex systems. First, elementary CA, such as the ones studied by Wolfram, will be presented in detail. Then, the role of CA as a tool to study statistical mechanics systems will be demonstrated through the simulation of the Ising spin model. Finally the expandable nature of CA will be explored

### Two-term tilting complexes and simple-minded systems of self-injective Nakayama algebras

, 2014

"... We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of simple modules under a stable equivalence, which is given by ..."

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We study the relation between simple-minded systems and two-term tilting complexes for self-injective Nakayama algebras. More precisely, we show that any simple-minded system of a self-injective Nakayama algebra is the image of the set of simple modules under a stable equivalence, which is given by the restriction of a standard derived equivalence induced by a two-term tilting complex. We achieve this by exploiting and connecting the mutation theories from the combinatorics of Brauer tree, configurations of stable translations quivers of type A, and triangulations of a punctured convex regular polygon.