Volume: 10, Issue: 2 (1999)
pp. 159-206 DOI: 10.1142/S0129167X99000070
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Abstract |
Full Text (PDF, 2,242KB)
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| Title: |
THE TENSOR PRODUCT IN THE THEORY OF FROBENNIUS MANIFOLDS |
| Author(s): |
RALPH M. KAUFMANN
Max-Planck-Institut Für Mathematik,
Bonn, Gottfried-Claren-Str. 26,
D-53225 Bonn, Germany
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| History: |
Received 5 June 1998
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| Abstract: |
We introduce the operation of forming the tensor product in the theory
of analytic Frobenius manifolds. Building on the results for formal
Frobenius manifolds which we extend to the additional structures of
Euler fields and flat identities, we prove that the tensor product of
pointed germs of Frobenius manifolds exists. Furthermore, we define
the notion of a tensor product diagram of Frobenius manifolds with
factorizable flat identity and prove the existence of such a diagram and
hence a tensor product Frobenius manifold. These diagrams and
manifolds are unique up to equivalence. Finally, we derive the special
initial conditions for a tensor product of semi-simple Frobenius
manifolds in terms of the special initial conditions of the
factors. |
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