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A path model for geodesics in Euclidean buildings and its applications to representation theory
path model for geodesics Euclidean buildings representation theory
2015/10/14
In this paper we give a combinatorial characterization of projections ofgeodesics in Euclidean buildings to Weyl chambers. We apply these results to the representation theory of complex reductive Lie ...
The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming...
Category equivalences involving graded modules over path algebras of quivers
Category equivalences path algebras of quivers Rings and Algebras
2011/9/14
Abstract: Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(k...
Simple Lie algebras arising from Leavitt path algebras
Leavitt path algebra simple Lie algebra commutator
2011/9/9
Abstract: For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily...
A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G contains at least one vertex from S. Denote by k(G)the minimum cardinality of a k-path vertex cover i...
Path subcoalgebras, finiteness properties and quantum groups
incidence coalgebra path coalgebra co-Frobenius coalgebra quasi-co-Frobenius coalgebra
2011/2/24
We study subcoalgebras of path coalgebras that are spanned by paths (called path subcoalgebras) and subcoalgebras of incidence coalgebras, and propose a unifying approach
for these classes.
Characterization Of Left Artinian Algebras Through Pseudo Path Algebras
Characterization Left Artinian Algebras Pseudo Path Algebras
2018/4/20
In this paper, using of pseudo path algebras, we generalize the Gabriel’s Theorem on elementary algebras to left Artinian algebras over a field k when the quotient algebra can be lifted,in particular,...
Generalized Path Coalgebra And Its Application To Dual Gabriel Theorem
Generalized Path Coalgebra Application Dual Gabriel Theorem
2018/4/20
As the duality of generalized path algebra, we firstly introduce the concept of generalized path coalgebra through assigning a k-coalgebra to each vertex of a given quiver. Some elementary properties ...