Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Symplectic C ∞ -algebras.
AU - Hamilton, Alastair
AU - Lazarev, Andrey
PY - 2008
Y1 - 2008
N2 - In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a C∞-algebra and does not generalize to algebras over other operads.
AB - In this paper we show that a strongly homotopy commutative (or C∞-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic C∞-algebra (an ∞-generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a C∞-algebra and does not generalize to algebras over other operads.
KW - Infinity-algebra
KW - cyclic cohomology
KW - Harrison cohomology
KW - symplectic structure
KW - Hodge decomposition
M3 - Journal article
VL - 8
JO - Moscow Mathematical Journal
JF - Moscow Mathematical Journal
SN - 1609-3321
IS - 3
ER -