Weak Frobenius manifolds

@article{Hertling1998WeakFM,
  title={Weak Frobenius manifolds},
  author={C. Hertling and Y. Manin},
  journal={arXiv: Quantum Algebra},
  year={1998}
}
We establish a new universal relation between the Lie bracket and $\circ$-multiplication of tangent fields on any Frobenius (super)manifold. We use this identity in order to introduce the notion of ``weak Frobenius manifold'' which does not involve metric as part of structure. As another application, we show that the powers of an Euler field generate (a half of) the Virasoro algebra on an arbitrary, not necessarily semisimple, Frobenius supermanifold. 
96 Citations
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Proposition. a). B is closed with respect to @BULLET and [, ] and hence forms a Poisson subalgebra. If A contains identity e
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Remark In the semisimple case the meaning of (19) is transparent: writing X = X i e i , we must have e i X j = 0 for i = j
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