Reduction techniques for the finitistic dimension

Edward L. Green; Chrysostomos Psaroudakis; Øyvind Solberg

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arXiv · 1808.03564

Reduction techniques for the finitistic dimension

Edward L. Green·Chrysostomos Psaroudakis·Øyvind Solberg

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Abstract

In this paper we develop new reduction techniques for testing the finiteness of the finitistic dimension of a finite dimensional algebra over a field. Viewing the latter algebra as a quotient of a path algebra, we propose two operations on the quiver of the algebra, namely arrow removal and vertex removal. The former gives rise to cleft extensions and the latter to recollements. These two operations provide us new practical methods to detect algebras of finite finitistic dimension. We illustrate our methods with many examples.

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Edward L. Green, Chrysostomos Psaroudakis, Øyvind Solberg. 2018-08-10. Reduction techniques for the finitistic dimension. https://arxiv.org/abs/1808.03564

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