MARC record from Internet Archive

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001 ocm02297010
003 OCoLC
005 20191204000903.0
008 760602s1976 riua b 000 0 eng
010 $a 76018784
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035 $a(OCoLC)2297010$z(OCoLC)1027344421$z(OCoLC)1059025319$z(OCoLC)1091885422
050 00 $aQA3$b.A57 no.173
055 3 $aQA251.5$b.D57 1976
082 0 $a512/.24
084 $aSI 810$2rvk
100 1 $aDlab, Vlastimil.
245 10 $aIndecomposable representations of graphs and algebras /$cVlastimil Dlab and Claus Michael Ringel.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$c℗♭1976.
300 $aiii, 57 pages :$billustrations ;$c26 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aMemoirs of the American Mathematical Society ;$vno. 173
504 $aIncludes bibliographical references (page 54).
505 00 $tIntroduction --$tValued graphs : Coxeter transformations, defect and listing of roots --$tRealization of valued graphs : the Coxeter functors --$tRepresentation of defect zero : general theory --$tSimple regular nonhomogeneous representations --$tHomogeneous representations --$tTables --$tAddendum.
520 $aI.N. Bernstein, I.M. Gelfand and V.A. Ponomarev have recently shown that the bijection, first observed by P. Gabriel, between the indecomposable representations of graphs ("quivers") with a positive definite quadratic form and the positive roots of this form can be proved directly. Appropriate functors produce all indecomposable representations from the simple ones in the same way as the canonical generators of the Weyl group produce all positive roots from the simple ones. This method is extended in two directions. In order to deal with all Dynkin diagrams rather than with those having single edges only, we consider valued graphs ("species"). In addition, we consider valued graphs with positive semi-definite quadratic form, i.e. extended Dynkin diagrams. The main result of the paper describes all indecomposable representations up to the homogeneous ones, of a valued graph with positive semi-definite quadratic form. These indecomposable representations are of two types: those of discrete dimension type, and those of continuous dimension type.
650 0 $aAssociative algebras.
650 0 $aRepresentations of algebras.
650 0 $aRepresentations of graphs.
650 7 $aAssociative algebras.$2fast$0(OCoLC)fst00819227
650 7 $aRepresentations of algebras.$2fast$0(OCoLC)fst01094934
650 7 $aRepresentations of graphs.$2fast$0(OCoLC)fst01094937
650 7 $aAlgebra.$2larpcal
650 7 $aAlgebra Associativa.$2larpcal
650 07 $aGraph.$2swd
650 7 $aUnzerlegbare Darstellung$2gnd
650 7 $aAlgebra$2gnd
650 7 $aGraph$2gnd
700 1 $aRingel, Claus Michael.$eauthor.
830 0 $aMemoirs of the American Mathematical Society ;$vno. 173.
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