04181nam 22007813 450 991097022390332120231110232526.09781470469122147046912X(MiAaPQ)EBC6852912(Au-PeEL)EBL6852912(CKB)20667667400041(RPAM)22491309(OCoLC)1295270068(EXLCZ)992066766740004120220117d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNon-Kissing Complexes and Tau-Tilting for Gentle Algebras1st ed.Providence :American Mathematical Society,2022.©2021.1 online resource (110 pages)Memoirs of the American Mathematical Society ;v.274"November 2021, volume 274, number 1343."Print version: Palu, Yann Non-Kissing Complexes and Tau-Tilting for Gentle Algebras Providence : American Mathematical Society,c2022 9781470450045 Includes bibliographical references.String modules -- The non-kissing complex -- The non-kissing lattice -- The non-kissing associahedron."We interpret the support -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously studied for quivers defined by a subset of the grid or by a dissection of a polygon. We then focus on the case when the non-kissing complex is finite. We show that the graph of increasing flips on its facets is the Hasse diagram of a congruence-uniform lattice. Finally, we study its g-vector fan and prove that it is the normal fan of a non-kissing associahedron"--Provided by publisher.Memoirs of the American Mathematical Society Combinatorial analysisRepresentations of algebrasPartially ordered setsCongruence latticesConvex polytopesAssociative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian ringsmscAssociative rings and algebras -- Representation theory of rings and algebras -- Representations of quivers and partially ordered setsmscCombinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theorymscCombinatorics -- Algebraic combinatorics -- Combinatorial aspects of simplicial complexesmscOrder, lattices, ordered algebraic structures -- Lattices -- Ideals, congruence relationsmscConvex and discrete geometry -- Polytopes and polyhedra -- $n$-dimensional polytopesmscCombinatorial analysis.Representations of algebras.Partially ordered sets.Congruence lattices.Convex polytopes.Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings.Associative rings and algebras -- Representation theory of rings and algebras -- Representations of quivers and partially ordered sets.Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory.Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of simplicial complexes.Order, lattices, ordered algebraic structures -- Lattices -- Ideals, congruence relations.Convex and discrete geometry -- Polytopes and polyhedra -- $n$-dimensional polytopes.512/.46512.4616G1016G2005E1005E4506B1052B11mscPalu Yann1801993Pilaud Vincent1801994Plamondon Pierre-Guy1801995MiAaPQMiAaPQMiAaPQBOOK9910970223903321Non-Kissing Complexes and Tau-Tilting for Gentle Algebras4347493UNINA