On a New Construction of Pseudo BL-Algebras

We present a new construction of a class pseudo BL-algebras, called kite pseudo BL-algebras. We start with a basic pseudo hoop $A$. Using two injective mappings from one set, $J$, into the second one, $I$, and with an identical copy $\overline A$ with the reverse order we construct a pseudo BL-algebra where the lower part is of the form $(\overline A)^J$ and the upper one is $A^I$. Starting with a basic commutative hoop we can obtain even a non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with non-commuting negations. We describe the construction, subdirect irreducible kite pseudo BL-algebras and their classification

Bases of quasi-hereditary covers of diagram algebras

We extend the the combinatorics of tableaux to the study of diagram algebras and give a uniform construction of their quasi-hereditary covers.Comment: Examples now include the classical Brauer, walled Brauer, and partition algebra

Kite Pseudo Effect Algebras

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least non-trivial normal ideal