Bulletin of the
Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2004; 41(3): 493-505

Printed September 1, 2004

Copyright © The Korean Mathematical Society.

Thomsen conditions on webs and their corresponding loops

Bokhee Im and In-Sook Oh

Chonnam National University, Chonnam National University

Abstract

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We introduce certain local Thomsen condition in a 3-web and prove that it is equivalent to the equation $a-(a-b)=b $ in its corresponding loop, where we denote the loop operation additively for convenience and simplicity, even though the loop is neither associative nor commutative. Also we interpret such local Thomsen condition using orthogonality of chains in a web.

Keywords: web, loop, chain reflection, Thomsen condition, local Thomsen condition

MSC numbers: 20N05, 53A60

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