In this paper we classify Ext-finite noetherian hereditary abelian categories over an algebraically closed field k satisfying Serre duality in the sense of Bondal and Kapranov. As a consequence we obtain a classification of saturated noetherian hereditary abelian categories. As a side result we show that when our hereditary abelian categories have no nonzero projectives or injectives, then the ...

In this paper we study wide subcategories. A full subcategory of R-modules is said to be wide if it is abelian and closed under extensions. Hovey [Hov01] gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms of certain specialisation closed subsets of Spec(R). We use this classification theorem to study K-theory and “Krull-Schmidt” decomp...

My principal references are [Serre:1965], [Reutenauer:1993], and [de Graaf:2000]. My interest in free Lie algebras has been motivated by the well known conjecture that Kac-Moody algebras can be defined by generators and relations analogous to those introduced by Serre for finite-dimensional semi-simple Lie algebras. I have had this idea for a long time, but it was coming across the short note [...

1. Yang-Baxter algebras (YBA), introduced in [1, 2, 3], generalize the wideknown FRT construction [4] in the following sense: to any numerical matrix solution R of the Yang-Baxter equation there is associated a bialgebra containing the FRT one as a sub-bialgebra. Generally, this construction may provide examples of (new) bialgebras and Hopf algebras [5]. In several aspects, there is some simila...

If (A,B) and (A′,B′) are co-t-structures of a triangulated category, then (A′,B′) is called intermediate if A ⊆ A′ ⊆ ΣA. Our main results show that intermediate co-t-structures are in bijection with two-term silting subcategories, and also with support τ -tilting subcategories under some assumptions. We also show that support τ -tilting subcategories are in bijection with certain finitely gener...

Are all subcategories of locally finitely presentable categories that are closed under limits and λ-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case λ = א0 the answer is affirmative also for all iso-full subcategories, i. e., those containing with every pair of objects all isomorphisms between them. We discuss...