Field-dependent homological behavior of finite dimensional algebras |
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Authors: | Birge Zimmermann Huisgen |
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Institution: | (1) Department of Mathematics, University of California, 93106 Santa Barbara, CA, USA |
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Abstract: | It is shown that the little finitistic dimension of a finite dimensional algebra, i.e., the supremum of the finite projective
dimensions attained on finitely generated modules, is not necessarily attained on a cyclic module. In general, arbitrarily
high numbers of generators are required. Moreover, it is demonstrated that this phenomenon may depend on the base fieldk. In fact, for each integerd>-3, there exists a quiver Γ with a set ρ of paths such that the little finitistic dimension of the finite dimensional algebrakΓ/<ρ> is attained on a cyclic module precisely when |k|≥d. By contrast, the global dimension of finite dimensional monomial relation algebras does not depend on the base field.
This research was partially supported by a grant from the National Science Foundation. |
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