Illinois Journal of Mathematics

Idempotent subquotients of symmetric quasi-hereditary algebras

Volodymyr Mazorchuk and Vanessa Miemietz

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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.

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Illinois J. Math., Volume 53, Number 3 (2009), 737-756.

First available in Project Euclid: 4 October 2010

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Primary: 16G10: Representations of Artinian rings 16D90: Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality 16W10: Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]


Mazorchuk, Volodymyr; Miemietz, Vanessa. Idempotent subquotients of symmetric quasi-hereditary algebras. Illinois J. Math. 53 (2009), no. 3, 737--756. doi:10.1215/ijm/1286212913.

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