Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects

Claude Roger

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 4, page 301-324
  • ISSN: 0044-8753

Abstract

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We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.

How to cite

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Roger, Claude. "Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects." Archivum Mathematicum 045.4 (2009): 301-324. <http://eudml.org/doc/250559>.

@article{Roger2009,
abstract = {We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.},
author = {Roger, Claude},
journal = {Archivum Mathematicum},
keywords = {supergeometry; odd symplectic manifolds; functional integral quantization; Graded Lie Algebras; Hochschild cohomology; supergeometry; odd symplectic manifold; functional integral quantization; graded Lie algebra; Hochschild cohomology},
language = {eng},
number = {4},
pages = {301-324},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects},
url = {http://eudml.org/doc/250559},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Roger, Claude
TI - Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 4
SP - 301
EP - 324
AB - We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.
LA - eng
KW - supergeometry; odd symplectic manifolds; functional integral quantization; Graded Lie Algebras; Hochschild cohomology; supergeometry; odd symplectic manifold; functional integral quantization; graded Lie algebra; Hochschild cohomology
UR - http://eudml.org/doc/250559
ER -

References

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