A New Construction Scheme Of Groups-Tilde Tensor

Entanglement state is one of the most important basic concepts in quantum informa-tion and quantum computation. It is because of the existence of entanglement that the quantum communication and quantum information cannot be deciphered and copy, and the local unitary equivalent is a important symmetry to keep entanglement. Research on local unitary equivalent greatly depends on the research on U(nm,C)/(U(n,C)(?)(m,C)) The understanding of the group U(n, C)(?) U(m, C) is one of the key research point.At the same time, from the perspective of group theory itself, how to construct the new group by a given group is one of the basic problem in group theory.In this paper, through minimum dimension faithful representation between the given groups G and H, Wc give a new construction scheme of groups-tilde tensor This definition has a generic property, and we can find that the tilde tensor defines a structure which similar to the Hopf algebra in the group category.Given two group G and H, we give the following results in this paper:1.Defined and proved that the rationality of G(?)H.2. Given some sufficient conditions to estimate the G(?)H is not homogeneous in GxH.3. Found the new algebra structure that similar to the hopf algebra structure in the group G though tilde tensor product.4. Given construction of tilde tensor about some group.5. Given some thoughts about stack and group representation.