On a New High Dimensional Weisfeiler-Lehman Algorithm
- Cite this article as:
- Evdokimov, S., Karpinski, M. & Ponomarenko, I. Journal of Algebraic Combinatorics (1999) 10: 29. doi:10.1023/A:1018672019177
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We investigate the following problem: how different can a cellular algebra be from its Schurian closure, i.e., the centralizer algebra of its automorphism group? For this purpose we introduce the notion of a Schurian polynomial approximation scheme measuring this difference. Some natural examples of such schemes arise from high dimensional generalizations of the Weisfeiler-Lehman algorithm which constructs the cellular closure of a set of matrices. We prove that all of these schemes are dominated by a new Schurian polynomial approximation scheme defined by the m-closure operators. A sufficient condition for the m-closure of a cellular algebra to coincide with its Schurian closure is given.