Thomsen conditions on webs and their corresponding loops
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 493-505
Published online September 1, 2004
Bokhee Im and In-Sook Oh
Chonnam National University, Chonnam National University
Abstract : 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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