# A Generalization of the Terwilliger Algebra

@article{Egge2000AGO, title={A Generalization of the Terwilliger Algebra}, author={Eric S. Egge}, journal={Journal of Algebra}, year={2000}, volume={233}, pages={213-252} }

Abstract P. M. Terwilliger (1992, J. Algebraic Combin.1, 363–388) considered the C -algebra generated by a given Bose Mesner algebra M and the associated dual Bose Mesner algebra M*. This algebra is now known as the Terwilliger algebra and is usually denoted by T. Terwilliger showed that each vanishing intersection number and Krein parameter of M gives rise to a relation on certain generators of T. These relations determine much of the structure of T, thought not all of it in general. To…

## 54 Citations

The Generalized Terwilliger Algebra and its Finite-dimensional Modules when d = 2

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Terwilliger [J. Algebraic Combin.1 (1992), 363–388] considered the C-algebra generated by a given Bose Mesner algebra M and the associated dual Bose Mesner algebra M*. This algebra is now known as…

On semisimple varietal Terwilliger algebras whose non-primary ideals are 1-dimensional

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The Terwilliger algebra of an almost-bipartite P- and Q-polynomial association scheme

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The Terwilliger Algebra of an Almost-Bipartite P- and Q-Polynomial Association Scheme

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Let Y denote a D-class symmetric association scheme with D ≥ 3, and suppose Y is almostbipartite Pand Q-polynomial. Let x denote a vertex of Y and let T = T (x) denote the corresponding Terwilliger…

The Terwilliger Algebra of the Hypercube

- MathematicsEur. J. Comb.
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An elementary proof that QD has the Q -polynomial property is given and T is a homomorphic image of the universal enveloping algebra of the Lie algebrasl2 (C).

The subconstituent algebra of a distance-regular graph; thin modules with endpoint one

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The Terwilliger Algebra Associated with a Set of Vertices in a Distance-Regular Graph

- Mathematics
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Let Γ be a distance-regular graph of diameter D. Let X denote the vertex set of Γ and let Y be a nonempty subset of X. We define an algebra τ = τ(Y). This algebra is finite dimensional and…

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