Special Issue: International Conference on Group Theory "Combinatorial, Geometric and Dynamical Aspects of Infinite Groups"; Guest Editors: Laurent Bartholdi, Tullio Ceccherini-Silberstein, Tatiana Smirnova-Nagnibeda, Andrzej ŻukNo Access

EXPONENT MATRICES AND TILED ORDERS OVER DISCRETE VALUATION RINGS

V. V. KIRICHENKO

Department of Mechanics and Mathematics, Kiev National Taras Shevchenko University, Vladimirskaya St. 64, Kiev 01033, Ukraine

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A. V. ZELENSKY

Department of Mathematics, Chernivcy National Yurij Fedkovich University, Universytetska St. 28, Chernivcy 58012, Ukraine

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, and

V. N. ZHURAVLEV

Department of Mechanics and Mathematics, Kiev National Taras Shevchenko University, Vladimirskaya St. 64, Kiev 01033, Ukraine

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https://doi.org/10.1142/S0218196705002724Cited by:4 (Source: Crossref)

Abstract

Exponent matrices appear in the theory of tiled orders over a discrete valuation ring. Many properties of such an order and its quiver are fully determined by its exponent matrix. We prove that an arbitrary strongly connected simply laced quiver with a loop in every vertex is realized as the quiver of a reduced exponent matrix. The relations between exponent matrices and finite posets, Markov chains, and doubly stochastic matrices are discussed.

Dedicated to Slava Grigorchuk on the occasion of his 50th birthday

Keywords:

AMSC: 16P40, 16G10

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