Symplectic C ∞ -algebras
نویسندگان
چکیده
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. 2000 Math. Subj. Class. 13D03, 13D10, 46L87, 55P62.
منابع مشابه
Quantum algebras and symplectic reflection algebras for wreath products
To a finite subgroup Γ of SL2(C), we associate a new family of quantum algebras which are related to symplectic reflection algebras for wreath products Sl o Γ via a functor of Schur-Weyl type. We explain that they are deformations of matrix algebras over rank-one symplectic reflection algebras for Γ and construct for them a PBW basis. When Γ is a cyclic group, we are able to give more informati...
متن کاملNilpotent symplectic alternating algebras II
In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class C of 2-Engel 3-groups of exponent 27 and under this correspondance we will see that the nilpotent algebras corre...
متن کاملSymplectic C∞-algebras
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 a...
متن کاملSymplectic C∞-algebras
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 a...
متن کاملCohomology algebras in symplectic, Kähler and algebraic geometry
We show a number of applications to geometry of the study of cohomology algebras of various kinds of manifolds. The main tool is Hodge theory, and we use it to show that projective complex manifolds are more restricted topologically than compact Kähler manifolds. We also make explicit numerous constraints satisfied by cohomology algebras of compact Kähler manifolds, making them very non generic...
متن کاملFe b 19 98 Level One Representations of Quantum Affine Algebras U q ( C ( 1 ) n )
We give explicit constructions of quantum symplectic affine algebras at level 1 using vertex operators.
متن کامل