Wykaz obszarów badawczych związanych z tagiem Rozmaitosci-algebr:
| # | Obszar badawczy | Dziedzina naukowa |
|---|---|---|
| 1 |
There is a one-to-one correspondence between nondegenerate set theoretical solutions of the Yang-Baxter equation and algebraic structures called biracks. On the other hand, biracks play an important role in knot theory. Biracks are algebras which have a structure of two one-sided quasigroups and satisfy some additional identities. So far, very little is known about such structures. The aim of the research will be to find new examples and constructions of biracks and to describe their algebraic characterization.
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| 2 |
My scientific interests include universal algebra and lattice theory, with special focus on their applications in other areas of mathematics, for example:
- ordered structures, e.g. algebras with semi-lattice operation, power algebras, algebras of subalgebras, as well as convex subsets for partially ordered sets of various types;
- algebraic structures related to geometry, knot theory, and set-theoretical solutions to the Yang-Baxter equation, such as quandles, racks or biracks, and in a wider context: one-sided quasigroups;
- barycentric algebras (algebraization of real convex sets) and their applications, e.g. in the modelling of complex systems;
- closure lattices (lattices of subclasses, convexity lattices, congruence lattices etc.) and their complexity;
- classes of structures defined by identities and quasi-identities.
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