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17
SUPPORT VARIETIES AND THE HOCHSCHILD COHOMOLOGY RING Modulo Nilpotence
, 2008
"... This paper is based on my talks given at the ‘41st ..."
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This paper is based on my talks given at the ‘41st
The Hochschild cohomology ring of a Class Of Special BISERIAL ALGEBRAS
, 2008
"... We consider a class of selfinjective special biserial algebras ΛN over a field K and show that the Hochschild cohomology ring of ΛN is a finitely generated Kalgebra. Moreover the Hochschild cohomology ring of ΛN modulo nilpotence is a finitely generated commutative Kalgebra of Krull dimension tw ..."
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Cited by 14 (7 self)
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We consider a class of selfinjective special biserial algebras ΛN over a field K and show that the Hochschild cohomology ring of ΛN is a finitely generated Kalgebra. Moreover the Hochschild cohomology ring of ΛN modulo nilpotence is a finitely generated commutative Kalgebra of Krull dimension two. As a consequence the conjecture of [18], concerning the Hochschild cohomology ring modulo nilpotence, holds for this class of algebras.
A BatalinVilkovisky algebra structure on the Hochschild cohomology of truncated polynomials
 University of Regina
, 2007
"... The main result of this paper is to calculate the BatalinVilkovisky structure of HH ∗ (C ∗ (KP n;R);C ∗ (KP n;R)) for K = C and H, and R = Z and any field; and shows that in the special case when M = CP 1 = S 2, and R = Z, this structure can not be identified with the BVstructure of H∗(LS 2; Z) co ..."
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Cited by 9 (0 self)
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The main result of this paper is to calculate the BatalinVilkovisky structure of HH ∗ (C ∗ (KP n;R);C ∗ (KP n;R)) for K = C and H, and R = Z and any field; and shows that in the special case when M = CP 1 = S 2, and R = Z, this structure can not be identified with the BVstructure of H∗(LS 2; Z) computed by Luc Memichi in [16]. However, the induced Gerstenhaber structures are still identified in this case. Moreover, according to a recent work of Y.Felix and J.Thomas [6], the main result of the present paper eventually calculates the BVstructure of the rational loop homology, H∗(LCP n; Q) and H∗(LHP n; Q), of projective spaces. 1
Radical cube zero weakly symmetric algebras and support varieties
, 2010
"... One of our main results is a classification all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via the Hochschild cohomology ring satisfying Dade’s Lemma. Along the way we give a characterization of when a finite dim ..."
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One of our main results is a classification all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via the Hochschild cohomology ring satisfying Dade’s Lemma. Along the way we give a characterization of when a finite dimensional Koszul algebra has such a theory of support in terms of the graded centre of the Koszul dual.
HOCHSCHILD COHOMOLOGY AND SUPPORT VARIETIES FOR TAME HECKE ALGEBRAS
, 2009
"... We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras. ..."
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We give a basis for the Hochschild cohomology ring of tame Hecke algebras. We then show that the Hochschild cohomology ring modulo nilpotence is a finitely generated algebra of Krull dimension 2, and describe the support varieties of modules for these algebras.
AN ALGORITHMIC APPROACH TO RESOLUTIONS
"... We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modied to construct minimal projective resolutions of linear modules over Koszul algebras. ..."
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Cited by 4 (2 self)
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We provide an algorithmic method for constructing projective resolutions of modules over quotients of path algebras. This algorithm is modied to construct minimal projective resolutions of linear modules over Koszul algebras.
HOCHSCHILD COHOMOLOGY OF SOCLE DEFORMATIONS OF A CLASS OF KOSZUL SELFINJECTIVE ALGEBRAS
, 2009
"... We consider the socle deformations arising from formal deformations of a class of Koszul selfinjective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence ..."
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We consider the socle deformations arising from formal deformations of a class of Koszul selfinjective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.
Realisability and Localisation
, 2007
"... Let A be a differential graded algebra with cohomology ring H ∗ A. A graded module over H ∗ A is called realisable if it is (up to direct summands) of the form H ∗ M for some differential graded Amodule M. Benson, Krause and Schwede have stated a local and a global obstruction for realisability. ..."
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Let A be a differential graded algebra with cohomology ring H ∗ A. A graded module over H ∗ A is called realisable if it is (up to direct summands) of the form H ∗ M for some differential graded Amodule M. Benson, Krause and Schwede have stated a local and a global obstruction for realisability. The global obstruction is given by the Hochschild class determined by the secondary multiplication of the A∞algebra structure of H ∗ A. In this thesis we mainly consider differential graded algebras A with gradedcommutative cohomology ring. We show that a finitely presented graded H ∗ Amodule X is realisable if and only if its plocalisation Xp is realisable for all graded prime ideals p of H ∗ A. In order to obtain such a localglobal principle also for the global obstruction, we define the localisation of a differential graded algebra A at a graded prime p of H ∗ A, denoted by Ap, and show the existence of a morphism of differential graded algebras inducing the canonical map H ∗ A → (H ∗ A)p in cohomology. The latter result actually holds in a much more general setting: we prove that every smashing localisation on the derived category of a differential graded algebra is induced by a morphism of differential graded algebras. Finally we discuss the relation between realisability of modules over the group cohomology ring and the Tate cohomology ring.