Representations of weakly triangular categories

A new class of locally unital and finite dimensional algebras over an arbitrary algebraically closed field is discovered. Each them admits upper weakly triangular decomposition, a generalization split decomposition. It established that the category -lfdmod left -modules fully stratified in sense Brundan-Stroppel. Moreover, semisimple if only its centralizer subalgebras associated to certain idempotent elements are semisimple. Furthermore, endofunctors defined so as give categorical actions some Lie on subcategory consisting all objects which have standard filtration. As application, we study representations either cyclotomic Brauer categories or Kauffman details, including explicit criteria semisimplicity field, being highest weight Brundan-Stroppel, Morita equivalence between direct sum infinitely many (degenerate) Hecke algebras. Finally, obtain categorifications classical limits coideal algebras, come from integrable modules sl ? ˆ e .