Koszul incidence algebras, affine semigroups, and Stanley–Reisner ideals
نویسندگان
چکیده
منابع مشابه
. A C ] 1 0 A pr 2 00 9 KOSZUL INCIDENCE ALGEBRAS , AFFINE SEMIGROUPS , AND STANLEY - REISNER IDEALS
We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the mo...
متن کاملLinear Koszul Duality and Affine Hecke Algebras
In this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras.
متن کاملIndecomposable Ideals in Incidence Algebras ⋆
The elements of a finite partial order P can be identified with the maximal indecomposable two-sided ideals of its incidence algebra A, and then for two such ideals, I ≺ J ⇐⇒ IJ 6= 0. This offers one way to recover a poset from its incidence algebra. In the course of proving the above, we classify all of the two-sided ideals of A. In contemporary physical theory, the concept of a “space” or, mo...
متن کاملWeak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups
Let S be a locally compact foundation semigroup with identity and be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of In this paper, we prove that X is invariantly complemented in if and only if the left ideal of has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...
متن کاملOn the Parameterization of Primitive Ideals in Affine Pi Algebras
In their fundamental studies of the finite dimensional representations of associative algebras, Artin and Procesi proved that the primitive ideals corresponding to irreducible n-dimensional representations (for fixed n, over an algebraically closed field) can be homeomorphically parameterized by a locally closed subset of the maximal spectrum of a suitably chosen affine commutative trace ring. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2010
ISSN: 0001-8708
DOI: 10.1016/j.aim.2010.02.005