Classification of commutative association schemes with almost commutative Terwilliger algebras
نویسندگان
چکیده
منابع مشابه
Classification of commutative association schemes with almost commutative Terwilliger algebras
We classify the commutative association schemes such that all nonprimary irreducible modules of their Terwilliger algebras are one-dimensional.
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Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in algebraic coding theory, and in areas as far afield as knot theory and numerical integration. This branch of the theory, viewed in this collection of surveys a...
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Let K be an infinite field and K〈X〉 = K〈X1, ..., Xn〉 the free associative algebra generated by X = {X1, ..., Xn} over K. It is proved that if I is a two-sided ideal of K〈X〉 such that the K-algebra A = K〈X〉/I is almost commutative in the sense of [3], namely, with respect to its standard N-filtration FA, the associated N-graded algebra G(A) is commutative, then I is generated by a finite Gröbner...
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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 properties of the Terwilliger algebra of the group association scheme of a finite group. We shall give bounds on the dimension of the Terwilliger algebra, and define triple regularity. Let G be a finit...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2010
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-010-0230-z