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A connection between varieties of quasigroups and graph decompositions

โœ Scribed by C.C. Lindner; C.A. Rodger

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
302 KB
Volume
272
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

In this paper we deรฟne an inรฟnite family of varieties of algebraic quasigroups, where for m ยฟ 3 the variety Vm satisรฟes a particular set of deรฟning identities Im. It is shown that the รฟnite members of Vm are precisely the quasigroups that can be obtained via a standard construction from certain decompositions of a complete graph into closed trails of lengths that each divide m. The result is presented from a graph theoretical perspective.

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## Abstract Let __X__ be a smooth complex projective variety and let __Z__ =(__s__ =0) be a smooth submanifold which is the zero locus of a section of an ample vector bundle __E__ of rank __r__ with dim __Z__ =dim __X__ โ€“__r__. We show with some examples that in general the Kleimanโ€“Mori cones NE(_