Topology Atlas | Conferences

Knots in Washington XXXVII
January 19-20, 2014
George Washington University
Washington, DC, USA

Organizers
Mieczyslaw K. Dabkowski (UT Dallas), Valentina Harizanov (GWU), Jozef H. Przytycki (GWU and UMCP), Yongwu Rong (GWU), Radmila Sazdanovic (NCSU), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Qualgebras and knotted 3-valent graphs
by
Victoria Lebed
Osaka City University
Coauthors: Seiichi Kamada

The quandle structure can be seen on the one hand as an algebraic counterpart of knots, and on the other as an axiomatic expression of the properties of conjugation in a group (where one forgets the multiplication and the inverse operations). In this talk we introduce the notion of qualgebra (= quandle + algebra), which is a quandle endowed with an additional "multiplication" operation, compatible with the quandle operation in a certain way. It can be seen on the one hand as an algebraic counterpart of 3-valent knotted graphs, and on the other as an axiomatic expression of the properties of conjugation and multiplication in a group (where one forgets the inverse operation). We discuss the properties of qualgebras, various examples (including those not coming from groups), and associated invariants of 3-valent graphs.

Date received: December 6, 2013

Copyright © 2013 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 # cbid-10.