Homology, Homotopy and Applications

Chicken or egg? A hierarchy of homotopy algebras

Füsun Akman

Full-text: Open access

Abstract

We start by clarifying and extending the multibraces notation, which economically describes substitutions of multilinear maps and tensor products of vectors. We give definitions and examples of weakly homotopy algebras, homotopy Gerstenhaber and Gerstenhaber bracket algebras, and homotopy Batalin-Vilkovisky algebras. We show that a homotopy algebra structure on a vector space can be lifted to its Hochschild complex, and also suggest an induction method to generate some of the explicit (weakly) homotopy Gerstenhaber algebra maps on a topological vertex operator algebra (TVOA), their existence having been indicated by Kimura, Voronov, and Zuckerman in 1996 (later amended by Voronov). The contention that this is the fundamental structure on a TVOA is substantiated by providing an annotated dictionary of weakly homotopy BV algebra maps and identities found by Lian and Zuckerman in 1993.

Article information

Source
Homology Homotopy Appl., Volume 7, Number 2 (2005), 5-39.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139839372

Mathematical Reviews number (MathSciNet)
MR2156305

Zentralblatt MATH identifier
1093.18007

Subjects
Primary: 18G50: Nonabelian homological algebra
Secondary: 18G55: Homotopical algebra

Citation

Akman, Füsun. Chicken or egg? A hierarchy of homotopy algebras. Homology Homotopy Appl. 7 (2005), no. 2, 5--39. https://projecteuclid.org/euclid.hha/1139839372


Export citation