This paper is devoted to new algebraic structures, called qualgebras and squandles. Topologically, they emerge as an algebraic counterpart of knotted 3-valent graphs, just like quandles can be seen as an "algebraization" of knots. Algebraically, they are modeled after groups with conjugation and multiplication/squaring operations. We discuss basic properties of these structures, and introduce and study the notions of qualgebra/squandle 2-cocycles and 2-coboundaries. Knotted 3-valent graph invariants are constructed by counting qualgebra/squandle colorings of graph diagrams, and are further enhanced using 2-cocycles. A classification of size 4 qualgebras/squandles and a description of their second cohomology groups are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-3,
author = {Victoria Lebed},
title = {Qualgebras and knotted 3-valent graphs},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {167-204},
zbl = {1316.05061},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-3}
}
Victoria Lebed. Qualgebras and knotted 3-valent graphs. Fundamenta Mathematicae, Tome 228 (2015) pp. 167-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm230-2-3/