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Generalized Cohomological Field Theories in the Higher Order Formalism.
- Source :
- Communications in Mathematical Physics; May2023, Vol. 399 Issue 3, p1439-1500, 62p
- Publication Year :
- 2023
-
Abstract
- In the classical Batalin–Vilkovisky formalism, the BV operator Δ is a differential operator of order two with respect to the commutative product. In the differential graded setting, it is known that if the BV operator is homotopically trivial, then there is a tree level cohomological field theory induced on the homology; this is a manifestation of the fact that the homotopy quotient of the operad of BV algebras by Δ is represented by the operad of hypercommutative algebras. In this paper, we study generalized Batalin–Vilkovisky algebras where the operator Δ is of the given finite order. In that case, we unravel a new interesting algebraic structure on the homology whenever Δ is homotopically trivial. We also suggest that the sequence of algebraic structures arising in the higher order formalism is a part of a "trinity" of remarkable mathematical objects, fitting the philosophy proposed by Arnold in the 1990s. [ABSTRACT FROM AUTHOR]
- Subjects :
- DIFFERENTIAL operators
HOMOLOGY theory
ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 399
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 163335254
- Full Text :
- https://doi.org/10.1007/s00220-022-04577-6