Two-sided projective resolutions, periodicity and local algebras

Beschreibung

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.

Autor*in

Stefanie Küpper

Themen in »Two-sided projective resolutions, periodicity and local algebras«

Darstellungstheorie / Representationtheory Hochschild Cohomologie / Hochschild cohomology Homologische Algebra / Homological algebra projektive Auflösungen / projective resolutions Lokale Algebren / local algebras

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