Algebra Seminar talk

Anatolij Dvurecenskij
On a New Construction of Kite Pseudo BL-algebras

Using two injections   lambda, rho :J → I   and an l-group G, we define an algebra whose universum is (G^+)^J below and (G^-)^I up. This universum can be endowed with a structure to be a pseudo BL-algebra.

Starting with an Abelian group, the resulting algebra, kite pseudo BL-algebra, can be non-commutative, and even a pseudo MV-alegbra or a pseudo BL-algebra with non-commuting two negations.

We present a characterization of subdirectly irreducible algebras and their classification. We show how this construction can be generalized using a basic pseudo hoop instead of an l-group.