Two-sided projective resolutions, periodicity and local algebras

By (author) Stefanie Kupper

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Extent: 75 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

Paperback (Published)

(December 2010)

ISBN: 9783832527242

6.65 x 9.45 inches

Price: $48.00

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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 A_{locto any finite dimensional algebra A. We try to derive information on the cohomology of A from the associated local algebra A_{loc, 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 A_{loc. 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 A_{mon, there are inequalities of the following kind: If the resolution of the monomial algebra A_{monis locally finite, then the resolution of A is locally finite. If the resolution of A_{monis locally periodic, then the resolution of A is either locally finite or locally almost periodic.

  • By (author) Stefanie Kupper

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