The Picard group of the Burnside ring.
The Prime Ideal Theorem in Non-Commutative Arithmetic.
The Prime Spectrum of the Enveloping Algebra of a Reductive Lie Algebra.
The primitivity of semigroup algebras of free products.
The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux.
The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...
The pure-projective ideal of a module category
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The radicalness of polynomial rings over nil rings.
The Radius of Convergence of Poincaré Series of Loop Spaces.
The rank of G0 for polycyclic group algebras
The Rational Invariants of the Tame Quivers.
The realization of input-output maps using bialgebras.
The relative dihedral homology of involutive algebras.
The relative Riemann-Roch theorem from Hochschild homology.
The representation dimension of domestic weakly symmetric algebras
Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras...
The representation theory and the branching graph for the family of Turaev algebras .
The representation theory of the Temperley-Lieb algebras.
The resultant of non-commutative polynomials
The ring of invariants of three -matrices over a field of prime characteristic.