Cubical Species and Nonassociative Algebras

Authors: Hetyei G.¹; Labelle G.²; Leroux P.²

Source: Advances in Applied Mathematics, Volume 21, Number 3, October 1998 , pp. 499-546(48)

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Abstract:

We lay down the foundations of a theory of cubical species, as a variant of Joyal's classical theory of species (A. Joyal, Adv. Math. 42 (1981), 1–82). Informally, a cubical species associates in a functorial way a set of structures to each hypercube. In this context, the hyperoctahedral groups replace the symmetric groups. We analyze cubical species, molecular cubical species, and basic operations among them, along with explicit examples. We show, in particular, that the cubical product gives rise, in a natural way, to a commutative nonassociative ring of formal power series. We conclude with a detailed analysis of this nonassociative ring. Copyright 1998 Academic Press.

Language: English

Document Type: Research article

Affiliations: 1: Mathematics Department, University of Kansas, Lawrence, Kansas, 66045-2142 2: Département de mathématiques, Université du Québec à Montréal, Montréal, Québec, H3C 3P8, Canada

Publication date: 1998-10-01