ИСТИНА

Multivalued groups arise in a fairly wide field of mathematical subjects: representation theory [1], discrete dynamical systems [2], algebraic geometry. The report will talk about a similar construction in the category of quandles, structures that have significant applications in knot theory and descrete integrable models. I will introduce the concept of an n-quandle, give some examples, describe the coset construction in this case, talk about a natural analogue of a group algebra for a quandle, and construct an n-corack bialgebra associated with a multivalued quandle. The report is based on the results of joint work with V. Bardakov, V. Buchstaber and T. Kozlovskaya in preparation.