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Pro-species of algebras I: Basic properties
Univ Stuttgart, Inst Algebra & Number Theory, Pfaffenwaldring 57, D-70569 Stuttgart, Germany.ORCID iD: 0000-0002-1216-4024
2017 (English)In: Algebras and Representation Theory, ISSN 1386-923X, E-ISSN 1572-9079, Vol. 20, no 5, p. 1215-1238Article in journal (Refereed) Published
Abstract [en]

In this paper, we generalise part of the theory of hereditary algebras to the context of pro-species of algebras. Here, a pro-species is a generalisation of Gabriel’s concept of species gluing algebras via projective bimodules along a quiver to obtain a new algebra. This provides a categorical perspective on a recent paper by Geiß et al. (2016). In particular, we construct a corresponding preprojective algebra, and establish a theory of a separated pro-species yielding a stable equivalence between certain functorially finite subcategories.

Place, publisher, year, edition, pages
2017. Vol. 20, no 5, p. 1215-1238
Keywords [en]
Species, Valued quiver, Preprojective algebra, Reflection functors, Separated quiver
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-359712DOI: 10.1007/s10468-017-9683-2ISI: 000412121200008OAI: oai:DiVA.org:uu-359712DiVA, id: diva2:1245352
Available from: 2018-09-05 Created: 2018-09-05 Last updated: 2018-09-05Bibliographically approved

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Külshammer, Julian

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