# Connes-Moscovici characteristic map is a Lie algebra morphism

Abstract : Let $H$ be a Hopf algebra with a modular pair in involution $(\Character,1)$. Let $A$ be a (module) algebra over $H$ equipped with a non-degenerated $\Character$-invariant $1$-trace $\tau$. We show that Connes-Moscovici characteristic map $\varphi_\tau:HC^*_{(\Character,1)}(H)\rightarrow HC^*_\lambda(A)$ is a morphism of graded Lie algebras. We also have a morphism $\Phi$ of Batalin-Vilkovisky algebras from the cotorsion product of $H$, $\text{Cotor}_H^*({\Bbbk},{\Bbbk})$, to the Hochschild cohomology of $A$, $HH^*(A,A)$. Let $K$ be both a Hopf algebra and a symmetric Frobenius algebra. Suppose that the square of its antipode is an inner automorphism by a group-like element. Then this morphism of Batalin-Vilkovisky algebras $\Phi:\text{Cotor}_{K^\vee}^*(\mathbb{F},\mathbb{F})\cong \text{Ext}_{K}(\mathbb{F},\mathbb{F}) \hookrightarrow HH^*(K,K)$ is injective.
Keywords :
Type de document :
Pré-publication, Document de travail
submitted version. Corollary 28 and Section 9 has been added. Section 9 computes the Batalin-Vilk.. 2010
Domaine :

https://hal.archives-ouvertes.fr/hal-00454042
Contributeur : Luc Menichi <>
Soumis le : jeudi 17 juin 2010 - 11:25:04
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 17:51:22

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Ext_Hochschild.pdf
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• HAL Id : hal-00454042, version 3
• ARXIV : 1002.1771

### Citation

Luc Menichi. Connes-Moscovici characteristic map is a Lie algebra morphism. submitted version. Corollary 28 and Section 9 has been added. Section 9 computes the Batalin-Vilk.. 2010. 〈hal-00454042v3〉

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