Representations of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="normal">Aut</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>A</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Γ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:math> acting on homogeneous components of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:mi>A</mml:mi><mml:mo stretchy="false">

Duffy, Colleen

doi:10.1016/j.aam.2008.05.003

Advances in Applied Mathematics

2009

DOI: 10.1016/j.aam.2008.05.003

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Representations of Aut(A(Γ)) acting on homogeneous components of A

Colleen Duffy

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 n-gons and the algebras Q n 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 ) ! .

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Cited by 4 publications

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Algebras associated to acyclic directed graphs

Retakh

Wilson

2009

Advances in Applied Mathematics

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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.1991 Mathematics Subject Classification. 05E05; 15A15; 16W30.

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Algebras associated to acyclic directed graphs

Retakh

Wilson

2009

Advances in Applied Mathematics

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Universal labeling algebras as invariants of layered graphs

Durst

2014

Advances in Applied Mathematics

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Abstract. In this work we will study the universal labeling algebra A(Γ), a related algebra B(Γ), and their behavior as invariants of layered graphs. We will introduce the notion of an upper vertex-like basis, which allows us to recover structural information about the graph Γ from the algebra B(Γ). We will use these bases to show that several classes of layered graphs are uniquely identified by their corresponding algebras B(Γ).

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Möbius Polynomials of Face Posets of Convex Polytopes

Jagadeesan

Durst

2016

Communications in Algebra

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Abstract. The Möbius polynomial is an invariant of ranked posets, closely related to the Möbius function. In this paper, we study the Möbius polynomial of face posets of convex polytopes. We present formulas for computing the Möbius polynomial of the face poset of a pyramid or a prism over an existing polytope, or of the gluing of two or more polytopes in terms of the Möbius polynomials of the original polytopes. We also present general formulas for calculating Möbius polynomials of face posets of simplicial polytopes and of Eulerian posets in terms of their f -vectors and some additional constraints.

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Representations of Aut(A(Γ)) acting on homogeneous components of A

Cited by 4 publications

References 8 publications

Algebras associated to acyclic directed graphs

Algebras associated to acyclic directed graphs

Universal labeling algebras as invariants of layered graphs

Möbius Polynomials of Face Posets of Convex Polytopes

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