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Search Results: 1 - 10 of 5257 matches for " Roland Berger "
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Non-homogeneous N-Koszul Algebras
Revista de la Uni?3n Matem??tica Argentina , 2007,
Abstract: this is a joint work with victor ginzburg [4] in which we study a class of associative algebras associated to finite groups acting on a vector space. these algebras are non-homogeneous n-koszul algebra generalizations of symplectic reflection algebras. we realize the extension of the n-koszul property to non-homogeneous algebras through a poincaré-birkhoff-witt property.
Centromeric, pericentromeric and heterochromatin abnormalities in chromosomal rearrangements of human leukemia
Berger Roland
Genetics and Molecular Biology , 2000,
Koszulity for nonquadratic algebras II
Roland Berger
Mathematics , 2003,
Abstract: It has been shown recently, in a joint work with Michel Dubois-Violette and Marc Wambst (see math.QA/0203035), that Koszul property of $N$-homogeneous algebras (as defined in the original paper) becomes natural in a $N$-complex setting. A basic question is to define the differential of the bimodule Koszul complex of an $N$-homogeneous algebra, e.g., for computing its Hochschild homology. The differential defined here uses $N$-complexes. That puts right the wrong differential presented in the original paper in a 2-complex setting. Actually, as we shall see, it is impossible to avoid $N$-complexes in defining the differential, whereas the bimodule Koszul complex is a 2-complex.
Gerasimov's theorem and N-Koszul algebras
Roland Berger
Mathematics , 2008, DOI: 10.1112/jlms/jdp005
Abstract: The paper is devoted to graded algebras having a single homogeneous relation. Using Gerasimov's theorem, a criterion to be N-Koszul is given, providing new examples. An alternative proof of Gerasimov's theorem for N=2 is given. Some related results on Calabi-Yau algebras are proved.
Combinatorics and N-Koszul algebras
Roland Berger
Mathematics , 2009,
Abstract: The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.
Calabi-Yau algebras viewed as deformations of Poisson algebras
Roland Berger,Anne Pichereau
Mathematics , 2011,
Abstract: We define a family of 3-Calabi-Yau algebras by potentials. For some of these algebras, we explicitly compute the Hochschild homology with the help of Poisson homology. The point is that the Poisson potential has non-isolated singularities.
Koszul and Gorenstein properties for homogeneous algebras
Roland Berger,Nicolas Marconnet
Mathematics , 2003,
Abstract: Koszul property was generalized to homogeneous algebras of degree N>2 in [5], and related to N-complexes in [7]. We show that if the N-homogeneous algebra A is generalized Koszul, AS-Gorenstein and of finite global dimension, then one can apply the Van den Bergh duality theorem [23] to A, i.e., there is a Poincare duality between Hochschild homology and cohomology of A, as for N=2.
Symplectic reflection algebras and non-homogeneous N-Koszul property
Roland Berger,Victor Ginzburg
Mathematics , 2005,
Abstract: From symplectic reflection algebras, some algebras are naturally introduced. We show that these algebras are non-homogeneous N-Koszul algebras, through a PBW theorem.
Poincare-Birkhoff-Witt Deformations of Calabi-Yau Algebras
Roland Berger,Rachel Taillefer
Mathematics , 2006,
Abstract: Recently, Bocklandt proved a conjecture by Van den Bergh in its graded version, stating that a graded quiver algebra (with relations) which is Calabi-Yau of dimension 3 is defined from a homogeneous potential W. In this paper, we prove that if we add to W any potential of smaller degree, we get a Poincare-Birkhoff-Witt deformation of A. Such PBW deformations are Calabi-Yau and are characterised among all the PBW deformations of A. Various examples are presented.
A criterion for homogeneous potentials to be 3-Calabi-Yau
Roland Berger,Andrea Solotar
Mathematics , 2012,
Abstract: We give a necessary and sufficient condition for an N-Koszul algebra defined by a homogeneous potential, to be 3-Calabi-Yau. As an application, we recover two families of 3-Calabi-Yau algebras recently appeared in the literature, by studying skew polynomial algebras over non-commutative quadrics.
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