Weak Frobenius manifolds

Details Weak Frobenius manifolds Weak Frobenius manifolds

1998-10-21

arxiv.org/abs/math/9810132v1

Mathematics

Quantum Algebra

9 pp, no figures

Scientific paper

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.

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