Sökning: "Koszul algebra"

Visar resultat 1 - 5 av 10 avhandlingar innehållade orden Koszul algebra.

1. 1. 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

3. 2. 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

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. Preprojective Algebras of d-Representation Finite Species with Relations

   Författare :Christoffer Söderberg; Martin Herschend; Grant Joseph; Uppsala universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : In this article we study the properties of preprojective algebras of representation finite species. To understand the structure of a preprojective algebra, one often studies its Nakayama automorphism. A complete description of the Nakayama automorphism is given by Brenner, Butler and King when the algebra is given by a path algebra. LÄS MER

7. 5. 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