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University Park
Altoona

Thursday, February 21, 2008
5:00 pm, 260 Hawthorn

Alissa Crans
Loyola Marymount University

Generalized Self-Distributivity

Self-distributive binary operations have appeared extensively in knot theory in recent years, specifically in algebraic structures called `quandles.' A quandle is a set equipped with two binary operations satisfying axioms that capture the essential properties of the operations of conjugation in a group. The self-distributive axioms of a quandle correspond to the third Reidemeister move in knot theory. Thus, quandles give a solution to the Yang-Baxter equation, which is an algebraic distillation of the third Reidemeister move. We formulate analogues of self-distributivity in the categories of coalgebras and Hopf algebras and use these to construct additional solutions to the
Yang-Baxter equation.

We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Fall 2007 semester: Young Choi and Aissa Wade.

 

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