Qualgebras and knotted 3-valent graphs

Victoria Lebed. "Qualgebras and knotted 3-valent graphs." Fundamenta Mathematicae 230.2 (2015): 167-204. <http://eudml.org/doc/282635>.

@article{VictoriaLebed2015,
abstract = {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.},
author = {Victoria Lebed},
journal = {Fundamenta Mathematicae},
keywords = {quandles; knotted 3-valent graphs; qualgebras; squandles; colorings; counting invariants; cocycle invariants; qualgebra cohomology},
language = {eng},
number = {2},
pages = {167-204},
title = {Qualgebras and knotted 3-valent graphs},
url = {http://eudml.org/doc/282635},
volume = {230},
year = {2015},
}

TY - JOUR
AU - Victoria Lebed
TI - Qualgebras and knotted 3-valent graphs
JO - Fundamenta Mathematicae
PY - 2015
VL - 230
IS - 2
SP - 167
EP - 204
AB - 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.
LA - eng
KW - quandles; knotted 3-valent graphs; qualgebras; squandles; colorings; counting invariants; cocycle invariants; qualgebra cohomology
UR - http://eudml.org/doc/282635
ER -