Tue, 19 Jan 2021, 1 pm MST
We study a class of algebras we regard as generalized rock-paper-scissors games. We show how to construct an infinite family of such algebras via group actions and that certain subsets of this family generate the varieties generated by hypertournament algebras, an n-ary analogue of tournament algebras. The group action construction allows us to find automorphisms of these algebras and determine their congruence lattices. We'll discuss how these results may aid in finding a (necessarily infinite) basis for the variety generated by tournament algebras, which to this author's knowledge remains an open problem.