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Two-sided projective resolutions, periodicity and local algebras
Stefanie Küpper
ISBN 978-3-8325-2724-2
75 pages, year of publication: 2010
price: 32.00 €
Two-sided projective resolutions, periodicity and local algebras
This book introduces a new point of view on two-sided projective resolutions of associative algebras. By gluing the vertices we associate a local algebra Aloc to any finite dimensional algebra A. We try to derive information on the cohomology of A from the associated local algebra Aloc, that is from the local equivalence class of A. For instance, the Anick-Green resolution is minimal for A if and only if it is so for Aloc. We can read off the relations of A whether there is a locally equivalent algebra that has a finite or a periodic bimodule resolution over itself.
Comparing an algebra A and an associated monomial algebra Amon, there are inequalities of the following kind: If the resolution of the monomial algebra Amon is locally finite, then the resolution of A is locally finite. If the resolution of Amon is locally periodic, then the resolution of A is either locally finite or locally almost periodic.
