Abstract
For any Chevalley (Bruhat) interval or face lattice of a polyhedral cone such that the Kazhdan-Lusztig polynomial or g-vector associated to each subinterval equals one, we construct an integral quasi-hereditary algebra C over the symmetric algebra of a naturally associated real vector space U. Under extension of scalars to the reals, C becomes isomorphic to a quasi-hereditary Koszul algebra with quasi-hereditary quadratic dual which has been previously defined by the author. We study a class of Koszul algebras such that both the algebra and its quadratic dual have properties similar to those of integral graded quasi-hereditary algebras, and show that for general reasons, C is a specialization under t ↦ 1 of a S(U′)-algebra of this type, where U′ = U ⊕ ℝt.
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© 1994 Springer Science+Business Media Dordrecht
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Dyer, M.J. (1994). Algebras Associated to Bruhat Intervals and Polyhedral Cones. In: Dlab, V., Scott, L.L. (eds) Finite Dimensional Algebras and Related Topics. NATO ASI Series, vol 424. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1556-0_6
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DOI: https://doi.org/10.1007/978-94-017-1556-0_6
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