Mathematische Zeitschrift

, Volume 285, Issue 3–4, pp 1091–1106 | Cite as

Homological embeddings for preprojective algebras

Article

Abstract

For a fixed finite dimensional algebra A, we study representation embeddings of the form \(mod(B)\rightarrow mod(A)\). Such an embedding is called homological, if it induces an isomorphism on all Ext-groups and weakly homological, if only Ext\(^1\) is preserved. In case A is a preprojective algebra of Dynkin type, we give an explicit classification of all weakly homological and homological embeddings. Furthermore, we show that for self-injective algebras a classification of homological embeddings becomes accessible once these algebras fulfil the Tachikawa conjecture.

Keywords

Homological embedding Preprojective algebra Self-injective algebra 

Mathematics Subject Classification

16E30 16G20 

Notes

Acknowledgments

The author is grateful to Martin Kalck for helpful discussions on the topic and for explaining some of the results in [19]. Moreover, the author would like to thank Julian Külshammer and Jorge Vitória for useful comments on an earlier version of this text, and the anonymous referee for helping to improve the presentation of the article. The author was supported by a grant within the DAAD P.R.I.M.E. program.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute for Algebra and Number TheoryUniversity of StuttgartStuttgartGermany

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