1,567 research outputs found
Symmetrization of Brace Algebras
We show that the symmetrization of a brace algebra structure yields the
structure of a symmetric brace algebra
Maurer-Cartan Elements and Cyclic Operads
First we argue that many BV and homotopy BV structures, including both
familiar and new examples, arise from a common underlying construction. The
input of this construction is a cyclic operad along with a cyclically invariant
Maurer-Cartan element in an associated Lie algebra. Using this result we
introduce and study the operad of cyclically invariant operations, with
instances arising in cyclic cohomology and equivariant homology. We
compute the homology of the cyclically invariant operations; the result being
the homology operad of , the uncompactified moduli spaces
of punctured Riemann spheres, which we call the gravity operad after Getzler.
Motivated by the line of inquiry of Deligne's conjecture we construct `cyclic
brace operations' inducing the gravity relations up-to-homotopy on the cochain
level. Motivated by string topology, we show such a gravity-BV pair is related
by a long exact sequence. Examples and implications are discussed in course.Comment: revised version to appear in the Journal of Noncommutative Geometr
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