The properties on F-manifold color algebras and pre-F-manifold color algebras

The properties on F-manifold color algebras and pre-F-manifold color algebras

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The concept of F-manifold algebras is an algebraic expression of F-manifolds.In this paper, we provide the definition of an F-manifold color algebra, which can be viewed as a natural generalization of an F-manifold algebra.We develop the representation theory Steamrollers of an F-manifold color algebra and show that F-manifold color algebras admitting non-degenerate symmetric bilinear forms are coherence F-manifold color algebras.The concept of pre-F-manifold color algebras is also presented, and using this definition read more one can construct F-manifold color algebras.

These results extend some properties of F-manifold algebras.