Inspired from research subjects in sub-riemannian geometry and metric geometry, we
propose uniform idempotent right quasigroups and emergent algebras as an alternative to …

In this paper, we give a geometric construction of the quantum group using Nakajima
categories, which were developed in Scherotzke ('Quiver varieties and self-injective …

Given a directed graph G, we can define a Hilbert space HG with basis indexed by the path
space of the graph, then represent the vertices of the graph as projections on HG and the …

Let GG be a locally compact, Hausdorff, étale groupoid whose unit space is totally
disconnected. We show that the collection A (G) A (G) of locally-constant, compactly …

This Ph. D. thesis is devoted to the study of the theory of quantization of Lie bialgebras and
related universal constructions. We give a new treatment of the Drinfeld associator arising …

The irreducible components of varieties parametrizing the finite dimensional representations
of a finite dimensional algebra Λ are explored, with regard to both their geometry and the …

Hereditary algebras are quasi-hereditary with respect to any adapted partial order on the
indexing set of the isomorphism classes of their simple modules. For any adapted partial …

Given a truncated path algebra A= 𝕜Q J k A=\BbbkQJ^k we prove that ϕ dim A= ϕ dim A op.
We also compute the ϕ-dimension of A as a function of the ϕ-dimension of 𝕜Q J 2 …

Quivers (directed graphs), species (a generalization of quivers) and their representations
play a key role in many areas of mathematics including combinatorics, geometry, and …

In this paper, we study ideal-and congruence-simpleness for the Leavitt path algebras of
directed graphs with coefficients in a commutative semiring S, establishing some …