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Infiltration of elaborate schemes
by
Scott Carter
University of South Alabama
Coauthors: Alissa Crans, Mohamed Elhamdadi, Pedro Lopes, Masahico Saito
The common thread to the Jacobi identity, the associative rule, Moufang loops, and the self-distributivity axiom is that an initial collection of elements is multiplied in various ways, and there is an identity among these possible products. Starting from the coboundary map for a function on a magma, we construct a second boundary in these various contexts such that compositions of these maps is zero. The context is quite general. In the case of Lie algebras and algebras, this method gives the ordinary cohomology theory. In the case of self-distributive structures, we have a cohomology that includes quandle cohomology.
Date received: November 13, 2006
Copyright © 2006 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # catp-12.