Recollements, sinks elimination and Leavitt path algebras

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• 作者：Roozbeh Hazrat ; Ju Huang
• 关键词：Leavitt path algebra ; Sink elimination ; Recollement
• 刊名：Archiv der Mathematik
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：107
• 期：6
• 页码：589-594
• 全文大小：458 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8938
• 卷排序：107

文摘

For Leavitt path algebras, we show that whereas removing sources from a graph produces a Morita equivalence, removing sinks gives rise to a recollement situation. In general, we show that for a graph \({E}\) and a finite hereditary subset \({H}\) of \({E^0}\), there is a recollement We record several corollaries.KeywordsLeavitt path algebraSink eliminationRecollementMathematics Subject ClassificationPrimary 16D70Secondary 18E35References1.Abrams G., Pino G. Aranda, Molina M. Siles: Finite-dimensional Leavitt path algebras. J. Pure Appl. Algebra 209, 753–762 (2007)MathSciNetCrossRefMATHGoogle Scholar2.G. Abrams, A. Louly, E. Pardo, and C. Smith, Flow invariants in the classification of Leavitt path algebras, J. Algebra 333 (2011), 202–23.3.F. Anderson and K. Fuller, Rings and categories of modules, second ed. GTM 13, Springer Verlag, New York, 1992.4.Ara P., Rangaswamy K.M.: Finitely presented simple modules over Leavitt path algebras. J. Algebra 417, 333–352 (2014)MathSciNetCrossRefMATHGoogle Scholar5.A. Aranda Pino and A. Nasr-Isfahani, Decomposable Leavitt path algebras for arbitrary graphs, Forum Math., in press (2015).6.A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux Pervers (Perverse sheaves), in: Analysis and Topology on Singular Spaces, I, Luminy, 1981, Asterisque 100 (1982), 5–171 (in French).7.H.X. Chen and C.C. Xi, Recollements of derived module categories, III: Finitustic dimensions, arXiv:1405.5090.8.E.T. Cline, B.J. Parshall, and L.L. Scott, Stratifying endomorphism algebras, Mem. Amer. Math. Soc. 124 (1996), viii+119 pp.9.Franjou V., Pirashvili T.: Comparison of abelian categories recollements. Doc. Math. 9, 41–56 (2004)MathSciNetMATHGoogle Scholar10.Kuhn N.: Generic representations of the finite general linear groups and the Steenrod algebra: II. K-Theory 8, 395–428 (1994)MathSciNetCrossRefMATHGoogle Scholar11.Rangaswamy K.M.: The theory of prime ideals of Leavitt path algebras over arbitrary graphs. J. Algebra 375, 73–96 (2013)MathSciNetCrossRefMATHGoogle Scholar12.Rangaswamy K.M.: On simple modules over Leavitt path algebras. J. Algebra 423, 239–258 (2015)MathSciNetCrossRefMATHGoogle Scholar13.Rangaswamy K.M.: Leavitt path algebras with finitely presented irreducible representations. J. Algebra 447, 624–648 (2016)MathSciNetCrossRefMATHGoogle Scholar14.R. Wisbauer, Foundations of modules and ring theory. A handbook for study and research, Revised and translated from the 1988 German edition: Algebra, Logic and Applications, 3. Gordon and Breach Science Publishers, Philadelphia, PA, 1991.Copyright information© Springer International Publishing 2016Authors and AffiliationsRoozbeh Hazrat1Ju Huang2Email author1.Western Sydney UniversitySydneyAustralia2.Fujian Normal UniversityFuzhouChina About this article CrossMark Print ISSN 0003-889X Online ISSN 1420-8938 Publisher Name Springer International Publishing About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00013-016-0967-2_Recollements, sinks elimination an", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00013-016-0967-2_Recollements, sinks elimination an", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. More information Accept Over 10 million scientific documents at your fingertips