1992/12/11 by Michael Penkava, Albert Schwarz, Penkava, Michael +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.hep-th/9212072
openalex publication_date 1992/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lian and Zuckerman proved that the homology of a topological chiral algebra can be equipped with the structure of a BV-algebra; \ie one can introduce a multiplication, an odd bracket, and an odd operator Δ having the same properties as the corresponding operations in Batalin-Vilkovisky quantization procedure. We give a simple proof of their results and discuss a generalization of these results to the non chiral case. To simplify our proofs we use the following theorem giving a characterization of a BV-algebra in terms of multiplication and an operator Δ: \em If A is a supercommutative, associative algebra and Δ is an odd second order derivation on A satisfying Δ2=0, one can provide A with the structure of a BV-algebra.