Using the tensor product variety introduced in [6] and [9], the complete structure of the tensor product of a finite number of integrable highest weight modules of Uq(sl 2) is recovered. In particular, the elementary basis, Lusztig's canonical basis, and the basis adapted to the decomposition of the tensor product into simple modules are all exhibited as distinguished elements of certain spaces...

Abstract. In this article, we study tensor product of Hilbert C∗-modules and Hilbert spaces. We show that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A⊗B-module E ⊗F , and we get more results. For Hilbert spaces H and K, we study tensor product of frames of subspaces for H an...

In this paper, we study some properties of the exterior tensor product on the category of modules. For this, we prove that the exterior tensor product of two permutation, endo-permutation, endo-trivial and endo-monomial modules are still permutation, endo-permutation endotrivial and endo-monomial modules respectively. Also, we prove that the cap of an exterior tensor product of two modules equa...

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

Using the tensor product variety introduced in [6] and [7], the complete structure of the tensor product of a finite number of integrable highest weight modules of Uq(sl 2) is recovered. In particular, the elementary basis, Lusztig's canonical basis, and the basis adapted to the decomposition of the tensor product into simple modules are all exhibited as distinguished elements of certain spaces...

We prove that the category of $\mathbb{Z}_2 ^n$-manifolds has all finite products. Further, we show a ^n$-manifold (resp., ^n$-morphism) can be reconstructed from its algebra global ^n$-functions morphism between ^n$-function algebras). These results are importance in study ^n$ Lie groups. The investigation is more challenging, since completed tensor product structure sheafs two not sheaf. rely...

Some prosperities of matrix product are presented in the paper, Kronecker product, Khatri-Rao product, Hadamard product and outer product are involved. And we get some results that a multilinear tensor can be represented by the product of matrix product for a three order tensor. For higher tensor, we conjure that the same results also hold. By the representation of matrix, we give an iterative ...

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...

The theory of crystal bases introduced by Kashiwara in [6] to study the category of integrable representations of quantized Kac–Moody Lie algebras has been a major development in the combinatorial approach to representation theory. In particular Kashiwara defined the tensor product of crystal bases and showed that it corresponded to the tensor product of representations. Later, in [7] he define...