(joint work with Prof. A.Kanel-Belov, Prof. E.Plotkin, Prof. E.Rips) It is well known that small cancellation groups and especially their generalizations provide a very powerful technique for constructing groups with unusual, and even exotic, properties, like for example, infinite Burnside groups and Tarski monster groups. In the present work we develop a small cancellation theory for associative algebras with a basis of invertible elements. We introduce a list of small cancellation conditions for a presentation of such associative algebras. We construct an explicit linear basis for these algebras. In parallel we show that our algebras possesses algorithmic properties similar to ones for groups with small cancellation groups. Namely, the equality problem in these algebras is solvable with the use of a certain analogue of Dehn’s algorithm. We do hope that being of interest as rings of new type by itself, these algebras will inherit useful practical properties known for small cancellation groups and, thus, they can be used for obtaining complicated algebras with the very specific properties.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
