Matches in SemOpenAlex for { <https://semopenalex.org/work/W4300178802> ?p ?o ?g. }
Showing items 1 to 51 of
51
with 100 items per page.
- W4300178802 abstract "This is the second in a series math.AG/0312190, math.AG/0410267, math.AG/0410268 on configurations in an abelian category A. Given a finite partially ordered set (I,<), an (I,<)-configuration (sigma,iota,pi) is a finite collection of objects sigma(J) and morphisms iota(J,K) or pi(J,K) : sigma(J) --> sigma(K) in A satisfying some axioms, where J,K are subsets of I. Configurations describe how an object X in A decomposes into subobjects. The first paper math.AG/0312190 defined configurations and studied moduli spaces of (I,<)-configurations in A, using the theory of Artin stacks. It proved well-behaved moduli stacks Obj_A, M(I,<)_A of objects and configurations in A exist when A is the abelian category coh(P) of coherent sheaves on a projective K-scheme P, or mod-KQ of representations of a quiver Q. Write CF(Obj_A) for the vector space of constructible functions on Obj_A. Motivated by Ringel-Hall algebras, we define an associative multiplication * on CF(Obj_A) using pushforwords and pullbacks along 1-morphisms between the M(I,<)_A, making CF(Obj_A) into an algebra. We also study representations of CF(Obj_A), the Lie subalgebra CF^ind(Obj_A) of functions supported on indecomposables, and other algebraic structures on CF(Obj_A). Then we generalize these ideas to stack functions SF(Obj_A), a universal generalization of constructible functions on stacks introduced in math.AG/0509722, containing more information. Under extra conditions on A we can define (Lie) algebra morphisms from SF(Obj_A) to some explicit (Lie) algebras, which will be important in the sequels on invariants counting t-(semi)stable objects in A." @default.
- W4300178802 created "2022-10-03" @default.
- W4300178802 creator A5023239521 @default.
- W4300178802 date "2005-03-02" @default.
- W4300178802 modified "2023-09-26" @default.
- W4300178802 title "Configurations in abelian categories. II. Ringel-Hall algebras" @default.
- W4300178802 doi "https://doi.org/10.48550/arxiv.math/0503029" @default.
- W4300178802 hasPublicationYear "2005" @default.
- W4300178802 type Work @default.
- W4300178802 citedByCount "0" @default.
- W4300178802 crossrefType "posted-content" @default.
- W4300178802 hasAuthorship W4300178802A5023239521 @default.
- W4300178802 hasBestOaLocation W43001788021 @default.
- W4300178802 hasConcept C118615104 @default.
- W4300178802 hasConcept C136119220 @default.
- W4300178802 hasConcept C136170076 @default.
- W4300178802 hasConcept C137212723 @default.
- W4300178802 hasConcept C168310172 @default.
- W4300178802 hasConcept C186921422 @default.
- W4300178802 hasConcept C202444582 @default.
- W4300178802 hasConcept C33923547 @default.
- W4300178802 hasConcept C67996461 @default.
- W4300178802 hasConcept C73373263 @default.
- W4300178802 hasConceptScore W4300178802C118615104 @default.
- W4300178802 hasConceptScore W4300178802C136119220 @default.
- W4300178802 hasConceptScore W4300178802C136170076 @default.
- W4300178802 hasConceptScore W4300178802C137212723 @default.
- W4300178802 hasConceptScore W4300178802C168310172 @default.
- W4300178802 hasConceptScore W4300178802C186921422 @default.
- W4300178802 hasConceptScore W4300178802C202444582 @default.
- W4300178802 hasConceptScore W4300178802C33923547 @default.
- W4300178802 hasConceptScore W4300178802C67996461 @default.
- W4300178802 hasConceptScore W4300178802C73373263 @default.
- W4300178802 hasLocation W43001788021 @default.
- W4300178802 hasLocation W43001788022 @default.
- W4300178802 hasLocation W43001788023 @default.
- W4300178802 hasOpenAccess W4300178802 @default.
- W4300178802 hasPrimaryLocation W43001788021 @default.
- W4300178802 hasRelatedWork W1626564065 @default.
- W4300178802 hasRelatedWork W2092350576 @default.
- W4300178802 hasRelatedWork W2807428903 @default.
- W4300178802 hasRelatedWork W2950797921 @default.
- W4300178802 hasRelatedWork W2950962716 @default.
- W4300178802 hasRelatedWork W2962949408 @default.
- W4300178802 hasRelatedWork W3126773016 @default.
- W4300178802 hasRelatedWork W4300840236 @default.
- W4300178802 hasRelatedWork W4301501389 @default.
- W4300178802 hasRelatedWork W4383469209 @default.
- W4300178802 isParatext "false" @default.
- W4300178802 isRetracted "false" @default.
- W4300178802 workType "article" @default.