Symmetric quasi-hereditary envelopes

Details Symmetric quasi-hereditary envelopes Symmetric quasi-hereditary envelopes

2008-12-17

arxiv.org/abs/0812.3286v1

Mathematics

Representation Theory

19 pages

Scientific paper

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 structure with respect to two opposite orders, that they have strong exact Borel and $\Delta$-subalgebras and the corresponding triangular decompositions.

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