We study the homotopy category K(InjA) of all injective A-modules InjA and derived category D(ModA) of the category ModA of all A-modules, where A is finite dimensional algebra over an algebraically closed field. We are interested in the algebra with discrete derived category (derived discrete algebra. For a derived discrete algebra A, we get more concrete properties of K(InjA) and D(ModA). The...

For any total category K , with defining adjunction ∨ a Y : K // set op , the expression W (A)(K) = set K op (K (A, ∨ −), [K,−]), where [K,−] is evaluation at K, provides a well-defined functor W : K // K̂ = set op . Also, there are natural transformations β : W ∨ // 1 K̂ and γ : ∨ W // 1K satisfying ∨ β = γ ∨ and βW = Wγ. A total K is totally distributive if ∨ has a left adjoint. We show that K ...

After the ring theoretic study of diierential operators in positive characteristic by S.U. Chase and S.P. Smith, B. Haastert started investigation of D-modules on smooth varieties in positive characteristic, and the work of R. BBgvad followed. The purpose of this paper is to complement some basics for further study. We x an algebraically closed eld k of positive characteristic p. All the variet...

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of the algebrization of logics [12]. A Priestley-style duality is established between the category of positive modal alg...

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of Abstract Algebraic Logic. In [4], a Priestley-style duality is established between the category of positive modal alg...

We continue the investigation of H-Galois extensions of linear categories, where H is a Hopf algebra. In our main result, the Theorem 2.2, we characterize this class of extensions in the case when H is finite dimensional. As an application, we prove a version of the Duality Theorem for crossed products with invertible cocycle. Introduction The duality theorems for actions and coactions originat...

Let M be a k-vector space and R ∈ End k(M ⊗M). In [10] we introduced and studied what we called the Hopf equation: R12R23 = R23R13R12. By means of a FRT type theorem, we have proven that the category HM H of H-Hopf modules is deeply involved in solving this equation. In the present paper, we continue to study the Hopf equation from another perspective: having in mind the quantum Yang-Baxter equ...