BERING LARSEN, Klaus. Odd Scalar Curvature in Batalin-Vilkovisky Geometry. Brno, Czech Republic: Habilitation thesis, Masaryk University, 2017, 36 pp.
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Basic information
Original name Odd Scalar Curvature in Batalin-Vilkovisky Geometry
Authors BERING LARSEN, Klaus.
Edition Brno, Czech Republic, 36 pp. 2017.
Publisher Habilitation thesis, Masaryk University
Other information
Original language English
Type of outcome Book on a specialized topic
Field of Study 10303 Particles and field physics
Country of publisher Czech Republic
Confidentiality degree is not subject to a state or trade secret
Organization unit Faculty of Science
Keywords in English Supermathematics; Supermanifolds; Odd Poisson Geometry; Darboux Theorem; Antibracket; Batalin-Vilkovisky Geometry; Curvature;
Tags NZ
Changed by Changed by: doc. Klaus Bering Larsen, Ph.D., učo 203385. Changed: 17/3/2019 16:22.
Abstract
After a brief introduction to Batalin-Vilkovisky (BV) formalism, we treat aspects of supermathematics in algebra and differential geometry, such as, stratification theorems, Frobenius theorem and Darboux theorem on supermanifolds. We use Weinstein's splitting principle to prove Darboux theorem for regular, possible degenerate, even and odd Poisson supermanifolds. Khudaverdian's nilpotent operator (which takes semidensities into semidensities of opposite Grassmann-parity) is introduced on both (i) an atlas of Darboux coordinates and (ii) in arbitrary coordinates. An odd scalar function is defined and it is shown that it has a geometric interpretation as an odd scalar curvature.
Links
GBP201/12/G028, research and development projectName: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku
Investor: Czech Science Foundation
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