R. Froberg, Determination of a class of Poincare series, Math Scand. 37 (1975), 29--39. Home/Search Document Not in Database Summary Related Articles Check |
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How to Shell a Monoid - Peeva, Reiner, Sturmfels (1997) (6 citations) (Correct)
....Proof. The algebra R = k[x 1 ; x n ] in OE (I ) is a Koszul algebra because in OE (I ) is generated by quadratic monomials. Using Corollary 2.2 and Remark 3.9 below, this implies that the Poincar e series of R equals the inverted Hilbert series (3. 3) On the other hand, Froberg [Fr] has shown that the non commutative algebra l ; y i y j y j y i i x l ;x i x j 62in OE (I ) carries the structure of a multigraded minimal free resolution of k over R, where a monomial m = y i 1 Delta Delta Delta y i r has homological degree r. The quadratic generators of the ....
....a minimal Grobner basis of this form: 5. 1) x i x i j Gamma x i 1 x i j Gamma1 Delta Y i j Gamma1 p=i 1 p ; 1 i n Gamma 2; 2 j n Gamma i: The underlined monomials span the initial ideal in OE (I ) A minimal free resolution of k over k[x 1 ; x n ] in OE (I ) is given in [Fr, Theorem in x3]. Our construction lifts this resolution to k[ using the specific relations (5.1) We first compute the total Betti numbers of k[ The following result improves Corollary 2.20 in [LS] Theorem 5.1. Let be a normal 2 dimensional monoid with n generators. Then i (k; k) n Gamma 2) for i ....
R. Froberg, Determination of a class of Poincar'e series, Math. Scand. 37 (1975), 29-39.
How To Shell A Monoid - Irena Peeva Victor (1997) (6 citations) (Correct)
....Proof. The algebra R = k[x 1 ; xn ] in OE (I ) is a Koszul algebra because in OE (I ) is generated by quadratic monomials. Using Corollary 2.2 and Remark 3.9 below, this implies that the Poincar e series of R equals the inverted Hilbert series (3. 3) On the other hand, Froberg [Fr] has shown that the non commutative algebra l ; y i y j y j y i i x l ;x i x j 62in OE (I ) carries the structure of a multigraded minimal free resolution of k over R, where a monomial m = y i 1 Delta Delta Delta y i r has homological degree r. The quadratic generators of the ....
....a minimal Grobner basis of this form: 5. 1) x i x i j Gamma x i 1 x i j Gamma1 Delta Y i j Gamma1 p=i 1 p ; 1 i n Gamma 2; 2 j n Gamma i: The underlined monomials span the initial ideal in OE (I ) A minimal free resolution of k over k[x 1 ; xn ] in OE (I ) is given in [Fr, Theorem in x3]. Our construction lifts this resolution to k[ using the specific relations (5.1) We first compute the total Betti numbers of k[ The following result improves Corollary 2.20 in [LS] Theorem 5.1. Let be a normal 2 dimensional monoid with n generators. Then i (k; k) n Gamma 2) for ....
R. Froberg, Determination of a class of Poincar'e series, Math. Scand. 37 (1975), 29-39.
How To Shell A Monoid - Peeva, Reiner, Sturmfels (1997) (6 citations) (Correct)
....ff i : Proof. The algebra R = k[x 1 ; xn ] in OE (I ) is a Koszul algebra because in OE (I ) is generated by quadratic monomials. Using Corollary 2.2 and Remark 3.10 below, this implies that the Poincar e series of R equals the inverted Hilbert series (3. 3) On the other hand, Froberg [Fr] has shown that the non commutative algebra (3.4) Rhy 1 ; yn i=hy 2 l ; y i y j y j y i i x 2 l ;x i x j 62in OE (I ) carries the structure of a multigraded minimal free resolution of k over R, where a monomial m = y i 1 Delta Delta Delta y i r has homological degree r. The ....
R. Froberg, Determination of a class of Poincar'e series, Math. Scand. 37 (1975), 29-39.
Koszul Algebras From Graphs and Hyperplane Arrangements - Shelton, Yuzvinsky (1996) (9 citations) (Correct)
....A graph algebra is an algebra given by a collection of relations of the form x i x j Gamma q i;j x j x i = 0 for some pairs (i; j) where q i;j 2 F . Graph algebras seem, by themselves, to form an interesting class of quadratic algebras. Froberg studied the Hilbert series of these algebras in [12] and proved that they are Koszul. Although we need only this result for deformations of U(A) we study the structure of these algebras more deeply. As a result we obtain a simple combinatorial formula for the Hilbert series of graph algebras. We also obtain another proof of Froberg s theorem. Now ....
....the images of the standard monomials form an F basis, this can only happen if a ff = 0 for every ff such that m ff x n is a standard monomial. Thus a 2 P j2C U ( Gamma)x j and the annihilator of x n Omega 1 F is therefore exactly P j2C U ( Gamma)x j . This proves the lemma. 2 Theorem 3. 8 [12] The algebra U ( Gamma) is Koszul for every edge labelled graph Gamma. Proof. We assume that Gamma has n vertices, labelled f1; ng, and a set of edges E. We proceed by induction on n, the case n = 1 being trivial. Let J = f1; n Gamma 1g and let C = fij(i; n) 2 e.g. By Lemma 3.5 ....
Froberg, R., Determination of a class of Poincare series, Math. Scand. 37 (1975), 29-39.
On the Charney-Davis and Neggers-Stanley Conjectures - Reiner, Welker (Correct)
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R. Froberg, Determination of a class of Poincare series, Math Scand. 37 (1975), 29--39.
On the Charney-Davis and Neggers-Stanley Conjectures - Reiner, Welker (Correct)
No context found.
R. Froberg, Determination of a class of Poincare series, Math Scand. 37 (1975), 29--39.
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