Abstract
We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasi-hereditary algebra. In the special case of rigid symmetric algebras, we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-hereditary structures with respect to two opposite orders, that they have strong exact Borel and
Δ
-subalgebras and the corresponding triangular decompositions.
Δ
-subalgebras and the corresponding triangular decompositions.
Original language | English |
---|---|
Pages (from-to) | 737-756 |
Number of pages | 20 |
Journal | Illinois Journal of Mathematics |
Volume | 53 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2009 |