References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Degenerations and other partial orders on the space of representations of algebrasPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)MasteroppgaveStudent thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

Institutt for matematiske fag , 2013. , 36 p.
##### Identifiers

URN: urn:nbn:no:ntnu:diva-21200Local ID: ntnudaim:10258OAI: oai:DiVA.org:ntnu-21200DiVA: diva2:632313
#####

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt396",{id:"formSmash:j_idt396",widgetVar:"widget_formSmash_j_idt396",multiple:true});
Available from: 2013-06-24 Created: 2013-06-24 Last updated: 2013-06-24Bibliographically approved

Let K be a field and¤be an artin K-algebra. Let r epd¤represent the set of all¤-modules with the length equal to a natural number d as a K-vector space. The set of modules r epd¤ is equipped with the action of the general linear group. The corresponding Zariski-topology for algebraically closed field K then induce a partial order on r epd¤, which is called degeneration order and it is denoted by ·deg . Here for M and N, ¤- modules, the notion M ·deg N mean that the orbit of N under the action of general linear group is contained in the closure of the orbit of M under the same group action. Another partial order on r epd¤ first showed by Riedtmann, is the virtual degeneration order, which is denoted by ·vdeg , are given by M ·vdeg N, if there is a ¤-module X such that M © X ·deg N © X. There are known examples where these two partial orders do not coincide. If K is an algebraically closed field, there is a geometric interpretation of these notions. However, there is also a module theoratical interpretation, which can be generalized to the general settings with K a commutative artin ring. Let ¡ be the Kronecker quiver 1â2 and ¤Æ Z2¡ be the path algebra of ¡ over the field Z2 with two elements. In this work all degenerations between isomrphism classes of modules over ¤ of dimension vector (1, 1), (2,2) and (3,3) are determined and the Hasse diagrams of the corresponding partial orders are given.

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1123",{id:"formSmash:lower:j_idt1123",widgetVar:"widget_formSmash_lower_j_idt1123",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1124_j_idt1126",{id:"formSmash:lower:j_idt1124:j_idt1126",widgetVar:"widget_formSmash_lower_j_idt1124_j_idt1126",target:"formSmash:lower:j_idt1124:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});