Related papers: Primitively generated Hall algebras

The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…

Group representable relation algebras play an important role in the study of representable relation algebras. The class of distributive involutive FL-algebras (DInFL-algebras) generalises relation algebras, as well as Sugihara monoids and…

We define a class of quadratic differential algebras which are generated as differential graded algebras by the elements of an Euclidean space. Such a differential algebra is a differential calculus over the quadratic algebra of its…

We introduce a category of cluster algebras with fixed initial seeds. This category has countable coproducts, which can be constructed combinatorially, but no products. We characterise isomorphisms and monomorphisms in this category and…

We give an explicit and essentially minimal list of defining relations of a Nichols algebra of diagonal type with finite root system. This list contains the well-known quantum Serre relations but also many new variations. A conjecture by…

C.M. Ringel defined Hall algebra associated with the category of representations of a quiver of Dynkin type and gave an explicit description of the structure constants of the corresponding Lie algebra. We utilize functorial properties of…

Let $\A$ be a finitary hereditary abelian category and $D(\A)$ be its reduced Drinfeld double Hall algebra. By giving explicit formulas in $D(\A)$ for left and right mutations, we show that the subalgebras of $D(\A)$ generated by…

This paper examines the category $\mathbf{Mat}_{\bullet}$ of pointed matroids and strong maps from the point of view of Hall algebras. We show that $\mathbf{Mat}_{\bullet}$ has the structure of a finitary proto-exact category - a…

Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that all of them can be exponentiated to cocycle matched pairs of…

A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…

For any prime number p and any positive real number {\alpha}, we construct a finitely generated group {\Gamma} with p-gradient equal to {\alpha}. This construction is used to show that there exist uncountably many pairwise non-commensurable…

We show that the full group C$^*$-algebra of the free product of two nontrivial countable amenable discrete groups, where at least one of them has more than two elements, is primitive. We also show that in many cases, this C$^*$-algebra is…

An algebraic quantum group is a multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication…

Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…

We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees and convergence groups. The latter category includes as a…

This is a survey on the state-of-the-art of the classification of finite-dimensional complex Hopf algebras. This general question is addressed through the consideration of different classes of such Hopf algebras. Pointed Hopf algebras…

We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…

Classical varieties were characterized by Lawvere as the categories with effective congruences and a varietal generator: an abstractly finite regular generator which is regularly projective (its hom-functor preserves regular epimorphisms).…

We construct a family of exact functors from the BGG category of representations of the Lie algebra sl to the category of finite-dimensional representations of the degenerate (or graded) affine Hecke algebra H of GL. These functors…

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity…