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1	The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras Norlén Jäderberg, Mika January 2023 (has links) Quasi-hereditary algebras are an important class of algebras with many appli-cations in representation theory, most notably the representation theory of semi-simple complex Lie-algebras. Such algebras sometimes admit an exact Borel sub-algebra, that is a subalgebra satisfying similar formal properties to the Borel sub-algebras from Lie theory. This thesis is divided into two parts. In the first part we classify quasi-hereditary algebras with two simple modules over perfect fields up to Morita equivalence, generalizing a similar result by Membrillo-Hernandez for thealgebraically closed case. In the second part, we take a poset X, a certain set M of constants, and a finite set ρ of paths in the Hasse-diagram of X and construct analgebra A(X, M, ρ) that generalizes the twisted double incidence algebras originally introduced by Deng and Xi. We provide necessary and sufficient conditions for this algebra to be quasi-hereditary when X is a tree, and we show that A(X, M, ρ) admits an exact Borel subalgebra when these conditions are satisfied. Following this, we compute the Ext-algebra of the standard modules of A(X, M, ρ). Algebras Finite-dimensional Partially ordered sets Modules Quasi-hereditary Ext-algebra Schur algebra Quiver Path algebra Categories Morita equivalence Yoneda product Standard module Homological algebra Cohomology Anick Chains Algebra and Logic Algebra och logik

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The Ext-Algebra of Standard Modules of Bound Twisted Double Incidence Algebras