Celebratio Mathematica — Schwarz

My life in science

Works connected to Robert Clark Penner

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M. Penkava and A. Schwarz: “On some algebraic structures arising in string theory,” pp. 219–227 in Perspectives in mathematical physics (Taiwan, summer 1992 and Los Angeles, winter 1992). Edited by R. C. Penner and S.-T. Yau. Conference Proceedings and Lecture Notes in Geometry and Topology 3. International Press (Boston), 1994. MR 1314668 Zbl 0871.17021 ArXiv hep-th/9212072 incollection

Lian and Zuckerman proved that the homology of a topological chiral algebra can be equipped with the structure of a BV-algebra; i.e., one can introduce a multiplication, an odd bracket, and an odd operator \( \Delta \) 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 \( \Delta \): If \( \mathcal{A} \) is a supercommutative, associative algebra and \( \Delta \) is an odd second order derivation on \( \mathcal{A} \) satisfying \( \Delta^2 = 0 \) , one can provide \( \mathcal{A} \) with the structure of a BV-algebra.

Michael Penkava	Related
Shing-Tung Yau	Related
Robert Clark Penner	Related