## Batalin–Vilkovisky algebras and two-dimensional topological field theories (1994)

Venue: | 265–285. AND ALGEBRAS 231 |

Citations: | 121 - 4 self |

### BibTeX

@INPROCEEDINGS{Getzler94batalin–vilkoviskyalgebras,

author = {E. Getzler},

title = {Batalin–Vilkovisky algebras and two-dimensional topological field theories},

booktitle = {265–285. AND ALGEBRAS 231},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract: By a Batalin-Vilkovisky algebra, we mean a graded commutative algebra A, together with an operator A: A.-+ A. such that A +1 2 = 0, and \_A,d \ — Aa is a graded derivation of A for all a e A. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions. We make use of a technique from algebraic topology: the theory of operads. Batalin-Vilkovisky algebras are a new type of algebraic structure on graded vector spaces, which first arose in the work of Batalin and Vilkovisky on gauge fixing in quantum field theory: a Batalin-Vilkovisky algebra is a differential graded commutative algebra together with an operator A: A.-+A such that A m+ί 2 = 0, and Δ{abc) = A(ab)c + (- V)^aA{bc) + (- l) (|α |-ίm