Discussiones Mathematicae General Algebra and Applications 23(1) (2003) 45-61
DOI: https://doi.org/10.7151/dmgaa.1063
DUALITY FOR SOME FREE MODES 1
| Krzysztof J. Pszczoła and Anna B. Romanowska
Faculty of Mathematics and Information Sciences |
Jonathan D.H. Smith
Department of Mathematics |
Abstract
The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.Keywords: duality, modes, affine spaces and their subreducts, barycentric algebras, convex sets, simplices, hypercubes.
2000 Mathematics Subject Classification: 18C05, 08A35, 08A05, 18A35.
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Received 4 March 2003
1The paper was written within the framework of COST Action 274. The third author acknowledges the hospitality and financial support received during the preparation of this paper from both the Stefan Banach International Mathematical Centre of the Polish Academy of Sciences and the Faculty of Mathematics and Information Sciences of Warsaw University of Technology.