This book is directed primarily at undergraduate and postgraduate students interested to get
acquainted with the representation theory of Lie algebras. The book treats the case of the …

This is the second of a series of four papers studying various generalisations of Khovanov's
diagram algebra. In this paper we develop the general theory of Khovanov's …

This paper studies quadratic and Koszul duality for modules over positively graded
categories. Typical examples are modules over a path algebra, which is graded by the path …

Tilting objects play a key role in the study of triangulated categories. A famous result due to
Iyama and Takahashi asserts that the stable categories of graded maximal Cohen …

We show that there exists a natural non-degenerate pairing of the homomorphism space
between two neighbor standard modules over a quasi-hereditary algebra with the first …

We determine the Ringel duals for all blocks in the parabolic versions of the BGG category O
ℒ associated to a reductive finite-dimensional Lie algebra. In particular, we find that, contrary …

A well-known conjecture says that every one-relator group is coherent. We state and partly
prove a similar statement for graded associative algebras. In particular, we show that every …

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul
DG algebras exist extensively, and have nice properties similar to the classic Koszul …

On a common generalization of Koszul duality and tilting equivalence Page 1 Advances in
Mathematics 227 (2011) 2327–2348 www.elsevier.com/locate/aim On a common …

We use the category of linear complexes of tilting modules for the BGG category, associated
with a semi-simple complex finite-dimensional Lie algebra g, to reprove in purely algebraic …