Sökning: "koszul"

Visar resultat 1 - 5 av 14 avhandlingar innehållade ordet koszul.

1. 1. Free loop spaces, Koszul duality and A-infinity algebras

   Författare :Kaj Börjeson; Alexander Berglund; Pascal Lambrechts; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Koszul duality; free loop spaces; a-infinity algebras; BV-algebras; string topology; Mathematics; matematik;

   Sammanfattning : This thesis consists of four papers on the topics of free loop spaces, Koszul duality and A∞-algebras. In Paper I we consider a definition of differential operators for noncommutative algebras. This definition is inspired by the connections between differential operators of commutative algebras, L∞-algebras and BV-algebras. LÄS MER

3. 2. Koszul duality for categories and a relative Sullivan-Wilkerson theorem

   Författare :Hadrien Espic; Gregory Arone; Alexander Berglund; Bjørn Dundas; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Koszul duality; categories; Yoneda algebra; operads; dg modules; homotopy automorphisms; Sullivan-Wilkerson; arithmetic group; matematik; Mathematics;

   Sammanfattning : This PhD thesis consists in a collection of three papers on Koszul duality of categories and on an analogue of the Sullivan-Wilkerson theorem for relative CW-complexes.In Paper I, we define a general notion of Koszul dual in the context of a monoidal biclosed model category. LÄS MER

4. 3. Structure and representations of certain classes of infinite-dimensional algebras

   Författare :Brendan Frisk Dubsky; Volodymyr Mazorchuk; Martin Herschend; Rolf Farnsteiner; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; infinite-dimensional algebras; representation theory; category O; koszul; koszulity; injections; dihedral; preprojective; young lattice; Mathematics; Matematik;

   Sammanfattning : We study several infinite-dimensional algebras and their representation theory. In Paper I, we study the category O for the (centrally extended) Schrödinger Lie algebra, which is an analogue of the classical BGG category O. We decompose the category into a direct sum of "blocks", and describe Gabriel quivers of these blocks. LÄS MER

5. 4. Centra of Quiver Algebras

   Författare :Elin Gawell; Christian Gottlieb; Qimh Xantcha; Jan Snellman; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; quiver; algebra; commutativity ideal; anti-commutativity ideal; non-commutative; partly commutative; partly anti-commutative; center; Koszul algebra; finitely generated; graded center; Hochschild cohomology; support variety; associative algebra; Mathematics; matematik;

   Sammanfattning : A partly (anti-)commutative quiver algebra is a quiver algebra bound by an (anti-)commutativity ideal, that is, a quadratic ideal generated by monomials and (anti-)commutativity relations. We give a combinatorial description of the ideals and the associated generator graphs, from which one can quickly determine if the ideal is admissible or not. LÄS MER

7. 5. Prop profiles of compatible Poisson and Nijenhuis structures

   Författare :Henrik Strohmayer; Sergei Merkulov; Gilles Halbout; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Koszul duality; resolutions; props; operads; compatible structures; MATHEMATICS; MATEMATIK; Mathematics; matematik;

   Sammanfattning : A prop profile of a differential geometric structure is a minimal resolution of an algebraic prop such that representations of this resolution are in one-to-one correspondence with structures of the given type. We begin this thesis with a detailed account of the algebraic tools necessary to construct prop profiles; we treat operads and props, and resolutions of these through Koszul duality. LÄS MER