Let g be a simple simply laced Lie algebra. In this paper two families of varieties associated to the Dynkin graph of g are described: tensor product and multiplicity varieties. These varieties are closely related to Nakajima’s quiver varieties and should play an important role in the geometric constructions of tensor products and intertwining operators. In particular, it is shown that the set ...

Relying on properties of the inductive tensor product, we construct cyclic type homology theories for certain nuclear algebras. In this context, we establish continuity theorems. We compute the periodic cyclic homology of the Schwartz algebra of p-adic GL(n) in terms of compactly supported de Rham cohomology of the tempered dual of GL(n). 1. Complete nuclear locally convex algebras Cyclic type ...

SUMMARY This paper proposes a novel signal estimation method that uses a tensor product expansion. When a bivariable function, which is expressed by two-dimensional matrix, is subjected to conventional tensor product expansion, two single variable functions are calculated by minimizing the mean square error between the input vector and its outer product. A tensor product expansion is useful for...

The properties and applications of kronecker product in quantum theory is studied thoroughly. The use of kronecker product in quantum information theory to get the exact spin Hamiltonian is given. The proof of non-commutativity of matrices, when kronecker product is used between them is given. It is shown that the non-commutative matrices after kronecker product are similar or they are similar ...

4 Derived Tensor 15 4.1 Tensor Product of Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Hoflat Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.3 Derived Tensor Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.4 Change of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Frame vectors in the tensor product of Hilbert spaces that accomplish phase retrieval can be characterized. In this article, we determine conditions under which may do retrieval. Given two frames always implies a frame spaces, particularly concentrate on finding for spaces.