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Graded traces and irreducible representations of Aut(A(Γ)) acting on grA(Γ) and grA(Γ
, 2008
"... Graded traces and irreducible representations of Aut(A(Γ)) acting on graded A(Γ) and A(Γ)! ..."
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Graded traces and irreducible representations of Aut(A(Γ)) acting on graded A(Γ) and A(Γ)!
Representations of Aut(A(Γ)) acting on homogeneous components of
 A(Γ) and A(Γ) ! , arXiv: 0804.4728
, 2008
"... Abstract. In this paper we will study the structure of algebras A(Γ) associated to two directed, layered graphs Γ. These are algebras associated with Hasse graphs of ngons and the algebras Qn related to pseudoroots of noncommutative polynomials. We will find the filtration preserving automorphism g ..."
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Cited by 3 (0 self)
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Abstract. In this paper we will study the structure of algebras A(Γ) associated to two directed, layered graphs Γ. These are algebras associated with Hasse graphs of ngons and the algebras Qn related to pseudoroots of noncommutative polynomials. We will find the filtration preserving automorphism group of these algebras and then we will find the multiplicities of the irreducible representations of Aut(A(Γ)) acting on the homogeneous components of A(Γ) and A(Γ) !.
ALGEBRAS ASSOCIATED TO DIRECTED ACYCLIC GRAPHS
, 707
"... Abstract. We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite directed acyclic graph admits a structure of a generalized layered graph. We construct linear bases in such algebras an ..."
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Cited by 2 (1 self)
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Abstract. We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite directed acyclic graph admits a structure of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings. In this paper we construct and study a class of algebras A(Γ) associated to generalized layered graphs Γ, i.e. directed graphs with a ranking function .  on their vertices. Therefore, each edge has a length l; if an edge e goes from a vertex v to a vertex w then l(e) = v  − w. Each
KOSZULITY OF SPLITTING ALGEBRAS ASSOCIATED WITH CELL COMPLEXES
, 810
"... Abstract. We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a twodimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two. Let Γ ..."
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Abstract. We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M. For a twodimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two. Let Γ = (V, E) be a layered graph (where V is the set of vertices and E is the set of edges). One may define an assoicated algebra, A(Γ), to be the algebra generated by E subject to the relations which state that (t − e1)(t − e2)...(t − ek) = (t − f1)(t − f2)...(t − fk)
QUADRATIC ALGEBRAS WITH EXT ALGEBRAS GENERATED IN TWO DEGREES
, 903
"... Abstract. We show that there exist nonKoszul graded algebras that appear to be Koszul up to any given cohomological degree. For any integer m ≥ 3 we exhibit a noncommutative quadratic algebra for which the corresponding bigraded Yoneda algebra is generated in degrees (1, 1) and (m, m + 1). The alg ..."
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Abstract. We show that there exist nonKoszul graded algebras that appear to be Koszul up to any given cohomological degree. For any integer m ≥ 3 we exhibit a noncommutative quadratic algebra for which the corresponding bigraded Yoneda algebra is generated in degrees (1, 1) and (m, m + 1). The algebra is therefore not Koszul but is mKoszul (in the sense of Backelin). These examples answer a question of Green and Marcos [3]. 1.
ALGEBRAS ASSOCIATED TO ACYCLIC DIRECTED GRAPHS
, 707
"... Abstract. We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in su ..."
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Cited by 1 (0 self)
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Abstract. We construct and study a class of algebras associated to generalized layered graphs, i.e. directed graphs with a ranking function on their vertices and edges. Each finite acyclic directed graph admits countably many structures of a generalized layered graph. We construct linear bases in such algebras and compute their Hilbert series. Our interest to generalized layered graphs and algebras associated to those graphs is motivated by their relations to factorizations of polynomials over noncommutative rings. By a generalized layered graph we mean a pair Γ = (G, .) where G = (V, E) is a directed graph and .  : V → Z≥0 satisfies v > w whenever v, w ∈ V and there is an edge e ∈ E from v to w. We call .  the rank function of Γ. We write l(e) = v  − w  and call this the
REPRESENTATIONS OF Aut(A(Γ)) ACTING ON HOMOGENEOUS COMPONENTS OF A(Γ) AND A(Γ)!
"... Abstract. In this paper we will study the structure of algebras A(Γ) associated to two directed, layered graphs Γ. These are algebras associated with Hasse graphs of ngons and the algebras Qn related to pseudoroots of noncommutative polynomials. We will find the filtration preserving automorphism g ..."
Abstract
 Add to MetaCart
Abstract. In this paper we will study the structure of algebras A(Γ) associated to two directed, layered graphs Γ. These are algebras associated with Hasse graphs of ngons and the algebras Qn related to pseudoroots of noncommutative polynomials. We will find the filtration preserving automorphism group of these algebras and then we will find the multiplicities of the irreducible representations of Aut(A(Γ)) acting on the homogeneous components of A(Γ) and A(Γ) !.