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Reduction techniques for the finitistic dimension

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arxiv 1808.03564 v1 pith:IITWGBG7 submitted 2018-08-10 math.RT math.CTmath.RA

Edward L. Green , Chrysostomos Psaroudakis , {O}yvind Solberg This is my paper · ORCID
classification math.RTmath.CTmath.RA
keywords algebradimensionfinitisticfinitelattermethodsoperationsreduction
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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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  1. Split bounded extension algebras and Han's conjecture

    math.KT 2019-08 accept novelty 7.0 of 10

    For split bounded extension algebras A = B ⊕ M, the algebra A satisfies Han's conjecture if and only if the subalgebra B does.

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