All Stable Characteristic Classes of Homological Vector Fields

Elena Mosman, Alexey Sharapov

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

An odd vector field Q on a supermanifold M is called homological, if Q2 = 0. The operator of Lie derivative LQ makes the algebra of smooth tensor fields on M into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator LQ and are represented by Q-invariant tensors made up of the homological vector field and a symmetric connection on M by means of the algebraic tensor operations and covariant differentiation.

Original languageEnglish
Pages (from-to)243-261
Number of pages19
JournalLetters in Mathematical Physics
Volume94
Issue number3
DOIs
Publication statusPublished - Dec 2010
Externally publishedYes

Fingerprint

Characteristic Classes
Vector Field
Tensor
tensors
Lie Derivative
Tensor Algebra
Supermanifold
Differential Algebra
algebra
Invariant
Operator
operators
Cohomology
homology
Odd
Algebra

Keywords

  • characteristic classes
  • gauge theories
  • Q-manifolds

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

All Stable Characteristic Classes of Homological Vector Fields. / Mosman, Elena; Sharapov, Alexey.

In: Letters in Mathematical Physics, Vol. 94, No. 3, 12.2010, p. 243-261.

Research output: Contribution to journalArticle

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