Batalin-Vilkovisky algebras and cyclic cohomology of Hopf algebras

By Luc Menichi. 2003

81 citations recorded by the source corpus.

We show that the Connes-Moscovici cyclic cohomology of a Hopf algebra equipped with a character has a Lie bracket of degree -2. More generally, we show that a "cyclic operad with multiplication" is a cocyclic module whose cohomology is a Batalin-Vilkovisky algebra and whose cyclic cohomology is a graded Lie algebra of degree -2. This explain why the Hochschild cohomology algebra of a symmetric algebra is a Batalin-Vilkovisky algebra.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/12e7cfeabca418f656649ff523844766e83ecee0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Guodong Zhou
2. Jue Le
3. Luc Menichi
4. Alexander Zimmermann
5. Amnon Yekutieli
6. Jon P. May

In Geometry and Topology

1. Guodong Zhou
2. Jue Le
3. Luc Menichi
4. Alexander Zimmermann
5. Amnon Yekutieli
6. Jon P. May

In Mathematical Physics

1. Guodong Zhou
2. Jue Le
3. Luc Menichi
4. Alexander Zimmermann

Citations in the corpus

• The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra (2014, background): “Menichi [28] gave a conceptual proof using the formalism of cyclic operads with multiplications; for another proof, see also [12].”
• On the Hochschild cohomology ring of tensor products of algebras (2014, background): “For different proofs of this fact, see [13] and [3].”
• Batalin-Vilkovisky algebra structures on Hochschild Cohomology (2007, background): “This theorem has been reproved and extended by many people [5, 8, 18, 20, 21, 22, 23, 28] (in chronological order).”