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}
}
  • E. Egge
  • Published 1 November 2000
  • Mathematics
  • Journal of Algebra
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… 
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References

SHOWING 1-10 OF 55 REFERENCES
The Subconstituent Algebra of an Association Scheme, (Part I)
AbstractWe introduce a method for studying commutative association schemes with “many” vanishing intersection numbers and/or Krein parameters, and apply the method to the P- and Q-polynomial schemes.
The Irreducible Modules of the Terwilliger Algebras of Doob Schemes
AbstractLet Y be any commutative association scheme and we fix any vertex x of Y. Terwilleger introduced a non-commutative, associative, and semi-simple C-algebraT=T(x) for Y and x in [4]. We call T
The Terwilliger Algebra of the Hypercube
TLDR
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 Terwilliger algebras of certain association schemes over the Galois rings of characteristic 4
TLDR
This paper replaces the finite field by a commutative local ring which is called a Galois ring of characteristic 4, and shows that most of the irreducible ℐ-modules have standard forms; otherwise, certain relations of the Jacobi sums hold.
THE TERWILLIGER ALGEBRAS OF GROUP ASSOCIATION SCHEMES
The Terwilliger algebra of an association scheme was introduced by Paul Terwilliger [7] in order to study P-and Q-polynomial association schemes. The purpose of this paper is to discuss in detail
THE TERWILLIGER ALGEBRAS OF THE GROUP ASSOCIATION SCHEMES OF S5 AND A5
Terwilliger proposed a method for studying commutative association schemes by introducing a non-commutative, semi-simple C-algebra, whose structure reflects the combinatorial nature of the
Bose-Mesner Algebras Related to Type II Matrices and Spin Models
A type II matrix is a square matrixW with non-zero complex entries such that the entrywise quotient of any two distinct rows of W sums to zero. Hadamard matrices and character tables of abelian
Homogeneous integral table algebras of degree three: a trilogy
Part I. Homogeneous Integral Table Algebras of Degree Three with a Faithful Real Element, H. I. Blau and B. Xu: Introduction Known facts and some consequences Homogeneous ITA's of arbitrary degree
...
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