RESEARCH ARTICLE

On the dimension of Kirichenko space

Makar Plakhotnyk

Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko Univ., Volodymyrska str., 64, 01033 Kyiv, Ukraine

Abstract: We introduce a notion of the Kirichenko space which is connected with the notion of Gorenstein matrix (see [2], ch. 14). Every element of Kirichenko space is an $n\times n$ matrix, whose elements are solutions of the equations $a_{i,j}+a_{j,\sigma (i)} =a_{i,\sigma(i)}$; $a_{1,i}=0$ for $i,j =1,\ldots, n$ determined by a permutation $\sigma$ which has no cycles of the length 1. We give a formula for the dimension of this space in terms of the cyclic type of $\sigma$.

Keywords: box, derived category, differential graded category.

MSC: 16E30,16E35

Received: 31.10.2005
Revised: 06.10.2006

Language: English

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