Related papers: Differential graded algebras over some reductive g…
In Part 1, we describe six projective-type model structures on the category of differential graded modules over a differential graded algebra A over a commutative ring R. When R is a field, the six collapse to three and are well-known, at…
We give the definition of a dg-division algebra, that is a concept of a differential graded algebra which may serve as an analogue of a division algebra. We classify them completely, and show that they are either acyclic or have…
Given a commutative algebra $A$ and a quotient $A$-algebra $A/I$, we construct a resolution of $A/I$ as an $A$-module such that it is also a differential graded (dg) algebra with divided powers (PD). This construction makes use of symmetric…
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these…
We develop the theory of a category ${\mathscr C}_A$ which is a generalisation to non-restricted ${\mathfrak g}$-modules of a category famously studied by Andersen, Jantzen and Soergel for restricted ${\mathfrak g}$-modules, where…
We develop a tensor categorical duality in the sprit of the Tannaka-Krein duality for the C*-algebras admitting the Yetter-Drinfeld module structure over a compact quantum group. Under this duality, given a reduced compact quantum group G,…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of…
Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates…
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…
We pose a new algebraic formalism for studying differential calculus in vector bundles. This is achieved by studying various functors of differential calculus over arbitrary graded commutative algebras (DCGCA) and applying this language to…
We consider self-injective finite-dimensional graded algebras admitting a triangular decomposition. In a preceding paper, we have shown that the graded module category of such an algebra is a highest weight category and has tilting objects…
The classification of the representations of the generalized deformed oscillator algebra is given together with several comments about possibility of introducing a coproduct structure in some type of deformed oscillator algebra.
In this paper we identify the cotangent to the derived stack of representations of a quiver $Q$ with the derived moduli stack of modules over the Ginzburg dg-algebra associated with $Q$. More generally, we extend this result to finite type…
In this thesis we describe the universal central extension of two important classes of so-called root-graded Lie algebras defined over a commutative associative unital ring $k.$ Root-graded Lie algebras are Lie algebras which are graded by…
We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent…
We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of $\mathop{\rm Ext}\nolimits$-finite hereditary abelian categories. Module categories of such…
To any trivalent plane graph embedded in the sphere, Casals and Murphy associate a differential graded algebra (dg-algebra), in which the underlying graded algebra is free associative over a commutative ring. Our first result is the…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
We study and relate categories of modules, comodules and contramodules over a representation of a small category taking values in (co)algebras, in a manner similar to modules over a ringed space. As a result, we obtain a categorical…