Graded-commutativity of the Yoneda product of Hopf bimodules.

Taillefer, Rachel

Displaying similar documents to “Graded-commutativity of the Yoneda product of Hopf bimodules.”

Coalgebraic Approach to the Loday Infinity Category, Stem Differential for $2 n$ -ary Graded and Homotopy Algebras

Mourad Ammar, Norbert Poncin (2010)

Annales de l’institut Fourier

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We define a graded twisted-coassociative coproduct on the tensor algebra the desuspension space of a graded vector space $V$ . The coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1-to-1 with sequences of multilinear maps on $V$ (resp. graded Loday structures on $V$ , sequences that we call Loday infinity structures on $V$ ). We prove a minimal model theorem for Loday infinity algebras and observe that the ${Lod}_{\infty}$ category contains the $L_{\infty}$ ...

From left modules to algebras over an operad: application to combinatorial Hopf algebras

Muriel Livernet (2010)

Annales mathématiques Blaise Pascal

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The purpose of this paper is two fold: we study the behaviour of the forgetful functor from $𝕊$ -modules to graded vector spaces in the context of algebras over an operad and derive the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for those Hopf algebras. Let $𝒪$ denote the forgetful functor from $𝕊$ -modules to graded vector spaces. Left modules over an operad $𝒫$ are treated as $𝒫$ -algebras in the category of $𝕊$ -modules. We generalize...

Local quasitriangular Hopf algebras.

Zhang, Shouchuan, Gould, Mark D., Zhang, Yao-Zhong (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Hochshild cohomology and equivalence of graded star products.

Ben Amar, N., Chaabouni, M. (2006)

Acta Mathematica Universitatis Comenianae. New Series

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The Hochschild cohomology of a closed manifold

Yves Felix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2004)

Publications Mathématiques de l'IHÉS

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Let M be a closed orientable manifold of dimension and $𝒞^{*} (M)$ be the usual cochain algebra on M with coefficients in a field. The Hochschild cohomology of M, $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is a graded commutative and associative algebra. The augmentation map $ε : 𝒞^{*} (M) \to 𝑘$ induces a morphism of algebras $I : H H^{*} (𝒞^{*} (M); 𝒞^{*} (M)) \to H H^{*} (𝒞^{*} (M); 𝑘)$ . In this paper we produce a chain model for the morphism I. We show that the kernel of I is a nilpotent ideal and that the image of I is contained in the center of $H H^{*} (𝒞^{*} (M); 𝑘)$ , which is in general quite small. The algebra $H H^{*} (𝒞^{*} (M); 𝒞^{*} (M))$ is expected to...

On Lie algebras in braided categories

Bodo Pareigis (1997)

Banach Center Publications

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The category of group-graded modules over an abelian group $G$ is a monoidal category. For any bicharacter of $G$ this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have $n$ -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are...

The ℤ₂-graded sticky shuffle product Hopf algebra

Robin L. Hudson (2006)

Banach Center Publications

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By abstracting the multiplication rule for ℤ₂-graded quantum stochastic integrals, we construct a ℤ₂-graded version of the Itô Hopf algebra, based on the space of tensors over a ℤ₂-graded associative algebra. Grouplike elements of the corresponding algebra of formal power series are characterised.

Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects

Claude Roger (2009)

Archivum Mathematicum

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We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.