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- W4226088618 abstract "In the classical Batalin–Vilkovisky formalism, the BV operator $$Delta $$ 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 $$Delta $$ is represented by the operad of hypercommutative algebras. In this paper, we study generalized Batalin–Vilkovisky algebras where the operator $$Delta $$ is of the given finite order. In that case, we unravel a new interesting algebraic structure on the homology whenever $$Delta $$ 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." @default.
- W4226088618 created "2022-05-05" @default.
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- W4226088618 date "2022-12-19" @default.
- W4226088618 modified "2023-09-30" @default.
- W4226088618 title "Generalized Cohomological Field Theories in the Higher Order Formalism" @default.
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- W4226088618 doi "https://doi.org/10.1007/s00220-022-04577-6" @default.
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