Deformations of Batalin–vilkovisky Algebras
نویسنده
چکیده
We show that a graded commutative algebra A with any square zero odd differential operator is a natural generalization of the Batalin–Vilkovisky algebra. While such an operator of order 2 defines a Lie algebra structure on A, an operator of an order higher than 2 (Koszul–Akman definition) leads to the structure of a strongly homotopy Lie algebra (L∞–algebra) on A. This allows us to give a definition of a Batalin–Vilkovisky algebra up-to homotopy. We also make an important conjecture generalizing Kontsevich formality theorem to the Batalin–Vilkovisky algebra level.
منابع مشابه
Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras
We analyze the algebraic and geometric structures of deformations of Schwarz type topological field theories. Deformations of the Chern-Simons-BF theory and BF theories in n dimensions are analyzed. Two dimensionanl theory induces the Poisson structure and three dimensional theory induces the Courant algebroid structure on the target space as a sigma model. We generalize these structures to hig...
متن کاملOperadic Formulation of Topological Vertex Algebras and Gerstenhaber or Batalin-vilkovisky Algebras
We give the operadic formulation of (weak, strong) topological vertex algebras, which are variants of topological vertex operator algebras studied recently by Lian and Zuckerman. As an application, we obtain a conceptual and geometric construction of the Batalin-Vilkovisky algebraic structure (or the Gerstenhaber algebra structure) on the cohomology of a topological vertex algebra (or of a weak...
متن کاملOn the quantum Batalin-Vilkovisky formalism and the renormalization of non linear symmetries
The most convenient tool to study the renormalization of a Lagrangian field theory invariant under non linear local or global symmetries is the proper solution to the master equation of the extended antifield formalism. It is shown that, from the knowledge of the BRST cohomology, it is possible to explicitly construct a further extension of the formalism containing all the observables of the th...
متن کاملIsomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket
One may introduce at least three different Lie algebras in any Lagrangian field theory : (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin-Vilkovisky antibracket, which has attracted considerable interest recently ; (ii) the Lie algebra of local conserved currents equipped with the Dickey bracket ; and (iii) the Lie algebra of conserved, integrated charges equip...
متن کاملFramed Discs Operads and Batalin–vilkovisky Algebras
The framed n-discs operad f Dn is studied as semidirect product of SO(n) and the little n-discs operad. Our equivariant recognition principle says that a grouplike space acted on by f Dn is equivalent to the n-fold loop space on an SO(n)-space. Examples of f D2-spaces are nerves of ribbon braided monoidal categories. We compute the rational homology of f Dn , which produces higher Batalin–Vilko...
متن کامل