The quiver of projectives in hereditary categories with Serre duality

Carl Fredrik Berg; Adam Christiaan van Roosmalen

doi:10.1016/j.jpaa.2009.09.014

The quiver of projectives in hereditary categories with Serre duality

Carl Fredrik Berg
, Adam Christiaan van Roosmalen^*

^*Corresponding author for this work

Norwegian University of Science and Technology
Max Planck Institute for Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Let k be an algebraically closed field and A a k-linear hereditary category satisfying Serre duality with no infinite radicals between the preprojective objects. If A is generated by the preprojective objects, then we show that A is derived equivalent to rep_k Q for a so-called strongly locally finite quiver Q. To this end, we introduce light cone distances and round trip distances on quivers which will be used to investigate sections in stable translation quivers of the form Z Q.

Original language	English
Pages (from-to)	1082-1094
Number of pages	13
Journal	Journal of Pure and Applied Algebra
Volume	214
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2009.09.014
Publication status	Published - Jul 2010
Externally published	Yes

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10.1016/j.jpaa.2009.09.014

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title = "The quiver of projectives in hereditary categories with Serre duality",

abstract = "Let k be an algebraically closed field and A a k-linear hereditary category satisfying Serre duality with no infinite radicals between the preprojective objects. If A is generated by the preprojective objects, then we show that A is derived equivalent to repk Q for a so-called strongly locally finite quiver Q. To this end, we introduce light cone distances and round trip distances on quivers which will be used to investigate sections in stable translation quivers of the form Z Q.",

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year = "2010",

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AU - Berg, Carl Fredrik

AU - van Roosmalen, Adam Christiaan

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N2 - Let k be an algebraically closed field and A a k-linear hereditary category satisfying Serre duality with no infinite radicals between the preprojective objects. If A is generated by the preprojective objects, then we show that A is derived equivalent to repk Q for a so-called strongly locally finite quiver Q. To this end, we introduce light cone distances and round trip distances on quivers which will be used to investigate sections in stable translation quivers of the form Z Q.

AB - Let k be an algebraically closed field and A a k-linear hereditary category satisfying Serre duality with no infinite radicals between the preprojective objects. If A is generated by the preprojective objects, then we show that A is derived equivalent to repk Q for a so-called strongly locally finite quiver Q. To this end, we introduce light cone distances and round trip distances on quivers which will be used to investigate sections in stable translation quivers of the form Z Q.

UR - https://www.scopus.com/pages/publications/74849106382

U2 - 10.1016/j.jpaa.2009.09.014

DO - 10.1016/j.jpaa.2009.09.014

M3 - Article

AN - SCOPUS:74849106382

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EP - 1094

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 7

ER -

The quiver of projectives in hereditary categories with Serre duality

Abstract

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