Related papers: Typability in partial groupoids
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
Given a partial action $\alpha$ of a connected groupoid $\mathcal{G}$ on an associative ring $A$ we investigate under what conditions the partial skew groupoid ring $A\star_{\alpha}\mathcal{G}$ can be realized as a partial skew group ring.…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We show that the group of proper projective similitudes of a totally decomposable algebra with involution of the first kind over a field of characteristic different from 2 is R-trivial.
We provide a characterization for multitwists satisfying the braid relation in the mapping class group of an orientable surface.
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.
We develop a method to give presentations of quantized function algebras of complex reductive groups. In particular, we give presentations of quantized function algebras of automorphism groups of finite dimensional simple complex Lie…
The theory of Nichols algebras of diagonal type is known to be closely related to that of semisimple Lie algebras. In this paper the connection between both theories is made closer. For any Nichols algebra of diagonal type invertible…
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…
The paper contains an application of van Kampen theorem for groupoids for computation of homotopy types of certain class of non-compact foliated surfaces obtained by gluing at most countably many strips $\mathbb{R}\times(0,1)$ with boundary…
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.
Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…
We develop a general theory of Clifford algebras for finite morphisms of schemes and describe applications to the theory of Ulrich bundles and connections to period-index problems for curves of genus 1.
We introduce a generalization of the Temperley--Lieb algebra. This generalization is defined by adding certain relations to the algebra of braids and ties. A specialization of this last algebra corresponds to one small Ramified Partition…
This is a survey of results on partially commutative groups and partially commutative algebras.
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.
In this paper we define a new product-like binary operation on directed graphs, and we discuss some of its properties. We also briefly discuss its application in constructing the subtyping relation in generic nominally-typed object-oriented…