The topic of this book, graded algebra, has developed in the past decade to a vast subject
with new applications in noncommutative geometry and physics. Classical aspects relating …

1.1 Let us first recall some definitions from [6]. A k-category N is a category whose morphism-
sets N (x, y) are endowed with k-vectorspace structures such that the composition maps are …

We introduce the intersection cohomology module of a matroid and prove that it satisfies
Poincaré duality, the hard Lefschetz theorem, and the Hodge–Riemann relations. As …

This study of graded rings includes the first systematic account of the graded Grothendieck
group, a powerful and crucial invariant in algebra which has recently been adopted to …

arXiv:0907.2985v2 [math.RT] 15 Feb 2010 Page 1 arXiv:0907.2985v2 [math.RT] 15 Feb 2010
Graded cellular bases for the cyclotomic Khovanov-Lauda-Rouquier algebras of type A Jun Hu1 …

In this paper we propose a new approach to tilting modules for reductive algebraic groups in
positive characteristic. We conjecture that translation functors give an action of the …

Let A=⊕ n≥ 0 An be a connected graded k-algebra and let Gr-A denote the category of
graded right A-modules with morphisms being graded homomorphisms of degree 0. If {τn∣ …

The aim of these lectures is to give a survey on the representation theory of Lie algebras of
reductive groups in prime characteristic. This theory is quite different from the corresponding …

We give a semi-small orthogonal decomposition of the Chow ring of a matroid M. The
decomposition is used to give simple proofs of Poincaré duality, the hard Lefschetz theorem …

The paper studies the interrelationship between coverings of finite directed graphs and
gradings of the path algebras associated to the directed graphs. To include gradings of all …