LEADER 05930nam 22008773 450 001 9910960757703321 005 20231110232547.0 010 $a9781470469146 010 $a1470469146 035 $a(MiAaPQ)EBC6852914 035 $a(Au-PeEL)EBL6852914 035 $a(CKB)20667668600041 035 $a(RPAM)22493609 035 $a(OCoLC)1295269396 035 $a(EXLCZ)9920667668600041 100 $a20220117d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aCell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2021. 215 $a1 online resource (154 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.274 300 $a"Volume 274, November 2021." 311 08$aPrint version: Margolis, Stuart Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry Providence : American Mathematical Society,c2022 9781470450427 320 $aIncludes bibliographical references and index. 327 $aLeft regular bands, hyperplane arrangements, oriented matroids and generalizations -- Regular CW complexes and CW posets -- Algebras -- Projective resolutions and global dimension -- Quiver presentations -- Quadratic and Koszul duals -- Injective envelopes for hyperplane arrangements, oriented matroids, CAT(0) cube complexes and COMs -- Enumeration of cells for CW left regular bands -- Cohomological dimension. 330 $a"The purpose of the present monograph is to further develop and deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A fairly complete picture of the representation theory for CW left regular bands is obtained"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aCW complexes 606 $aSemigroups 606 $aPartially ordered sets 606 $aRepresentations of algebras 606 $aCombinatorial analysis 606 $aCombinatorial geometry 606 $aGroup theory and generalizations -- Semigroups -- Representation of semigroups; actions of semigroups on sets$2msc 606 $aAssociative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings$2msc 606 $aCombinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory$2msc 606 $aConvex and discrete geometry -- Discrete geometry -- Arrangements of points, flats, hyperplanes$2msc 606 $aConvex and discrete geometry -- Discrete geometry -- Oriented matroids$2msc 606 $aAssociative rings and algebras -- Rings and algebras arising under various constructions -- Quadratic and Koszul algebras$2msc 606 $aGroup theory and generalizations -- Semigroups -- Semigroup rings, multiplicative semigroups of rings$2msc 606 $aConvex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.)$2msc 606 $aAssociative rings and algebras -- Homological methods -- Homological dimension$2msc 615 0$aCW complexes. 615 0$aSemigroups. 615 0$aPartially ordered sets. 615 0$aRepresentations of algebras. 615 0$aCombinatorial analysis. 615 0$aCombinatorial geometry. 615 7$aGroup theory and generalizations -- Semigroups -- Representation of semigroups; actions of semigroups on sets. 615 7$aAssociative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings. 615 7$aCombinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory. 615 7$aConvex and discrete geometry -- Discrete geometry -- Arrangements of points, flats, hyperplanes. 615 7$aConvex and discrete geometry -- Discrete geometry -- Oriented matroids. 615 7$aAssociative rings and algebras -- Rings and algebras arising under various constructions -- Quadratic and Koszul algebras. 615 7$aGroup theory and generalizations -- Semigroups -- Semigroup rings, multiplicative semigroups of rings. 615 7$aConvex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.). 615 7$aAssociative rings and algebras -- Homological methods -- Homological dimension. 676 $a512/.27 676 $a512.27 686 $a20M30$a16G10$a05E10$a52C35$a52C40$a16S37$a20M25$a52B05$a16E10$2msc 700 $aMargolis$b Stuart$01800391 701 $aSaliola$b Franco$01800392 701 $aSteinberg$b Benjamin$0472320 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910960757703321 996 $aCell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry$94345153 997 $aUNINA