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Retractions and Gorenstein Homological Properties
, 2014
"... We associate to a localizable module a left retraction of algebras; it is a homological ring epimorphism that preserves singularity categories. We study the behavior of left retractions with respect to Gorenstein homological properties (for example, being Gorenstein algebras or CMfree algebras). W ..."
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Cited by 4 (1 self)
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We associate to a localizable module a left retraction of algebras; it is a homological ring epimorphism that preserves singularity categories. We study the behavior of left retractions with respect to Gorenstein homological properties (for example, being Gorenstein algebras or CMfree algebras
HOMOLOGICAL PROPERTIES OF BIGRADED ALGEBRAS
, 2001
"... We investigate the x and yregularity of a bigraded Kalgebra R as introduced in [2]. These notions are used to study asymptotic properties of certain finitely generated bigraded modules. As an application we get for any equigenerated graded ideal I upper bounds for the number j0 for which reg(I j) ..."
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Cited by 10 (0 self)
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We investigate the x and yregularity of a bigraded Kalgebra R as introduced in [2]. These notions are used to study asymptotic properties of certain finitely generated bigraded modules. As an application we get for any equigenerated graded ideal I upper bounds for the number j0 for which reg(I j
Homological properties of OrlikSolomon algebras
"... ABSTRACT. The OrlikSolomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first we study homological properties of Emodules as e.g. complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our result ..."
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Cited by 5 (3 self)
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ABSTRACT. The OrlikSolomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first we study homological properties of Emodules as e.g. complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our
Some homological properties of the category O
"... In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an explicit conjecture relating the result to Lusztig’s afunction is formula ..."
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Cited by 16 (8 self)
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In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an explicit conjecture relating the result to Lusztig’s afunction is formulated (and proved for type A). The second part deals with the extension algebra of Verma modules. It is shown that this algebra is in a natural way Z²graded and that it has two Zgraded Koszul subalgebras. The dimension of the space Ext 1 into the projective Verma module is determined. In the last part several new classes of Koszul modules and modules, represented by linear complexes of tilting modules, are constructed.
Action recognition in the premotor cortex
 Brain
, 1996
"... We recorded electrical activity from 532 neurons in the rostral part of inferior area 6 (area F5) of two macaque monkeys. Previous data had shown that neurons of this area discharge during goaldirected hand and mouth movements. We describe here the properties of a newly discovered set of F5 neurons ..."
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Cited by 671 (47 self)
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We recorded electrical activity from 532 neurons in the rostral part of inferior area 6 (area F5) of two macaque monkeys. Previous data had shown that neurons of this area discharge during goaldirected hand and mouth movements. We describe here the properties of a newly discovered set of F5
QUASIHEREDITARY ALGEBRAS: HOMOLOGICAL PROPERTIES
"... Throughout, we let A be a finitedimensional algebra over an algebraically closed field k1. We fix a finite, partially ordered set (I,≤) with (S(i))i∈I being a complete set of representatives for the isomorphism classes of the simple Amodules. For each i ∈ I, let P (i) and I(i) be the projective co ..."
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Throughout, we let A be a finitedimensional algebra over an algebraically closed field k1. We fix a finite, partially ordered set (I,≤) with (S(i))i∈I being a complete set of representatives for the isomorphism classes of the simple Amodules. For each i ∈ I, let P (i) and I(i) be the projective cover and the injective hull of S(i), respectively. We will be working in the category modA of finitedimensional Amodules. The JordanHölder multiplicity of S(i) in M will be denoted [M: S(i)]. As in [2], we consider the standard modules (∆(i))i∈I, satisfying (a) Top(∆(i)) ∼ = S(i) and [∆(i):S(i)] = 1, as well as (b) [∆(i):S(j)] = 0 for j 6 ≤ i. The full subcategory of modA consisting of the ∆good modules will be denoted F(∆). Thus, each object M ∈ F(∆) affords a filtration, whose factors are standard modules. We let (M: ∆(i)) be the multiplicity of ∆(i) in M. As usual, ΩA denotes the Heller operator of modA. Definition. The algebra A is quasihereditary if (a) each P (i) is ∆good, and (b) (P (i):∆(i)) = 1 and (P (i):∆(j)) = 0 for i 6 ≤ j. If, in addition, there exists a duality D: modA − → modA with D(S(i)) ∼ = S(i), then A is called
Results 1  10
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2,607