• Title, Summary, Keyword: tensor product

Search Result 106, Processing Time 0.034 seconds

COHOMOLOGY RING OF THE TENSOR PRODUCT OF POISSON ALGEBRAS

  • Zhu, Can
    • Journal of the Korean Mathematical Society
    • /
    • v.57 no.1
    • /
    • pp.113-129
    • /
    • 2020
  • In this paper, we study the Poisson cohomology ring of the tensor product of Poisson algebras. Explicitly, it is proved that the Poisson cohomology ring of tensor product of two Poisson algebras is isomorphic to the tensor product of the respective Poisson cohomology ring of these two Poisson algebras as Gerstenhaber algebras.

A semi-exact in tensor product

  • Bae, Chul-Kon;Lee, Im-Suk;Min, Kang-Joo
    • The Mathematical Education
    • /
    • v.12 no.1
    • /
    • pp.1-3
    • /
    • 1973
  • In this paper, we want to verify some properties in tensor product. It is interesting to think semi-exact sequence in tensor Product by [3]. Moreover no hardness is there in process and we want to discuss the commutativity in tensor product. For a certain semi-exact sequence, if we product arbitrary Abelian group for each group then the tensor Product will do or not. Here, we have positive answer. At first we define the semi-exact sequence as following.

  • PDF

GENERALIZATION ON PRODUCT DEGREE DISTANCE OF TENSOR PRODUCT OF GRAPHS

  • PATTABIRAMAN, K.
    • Journal of applied mathematics & informatics
    • /
    • v.34 no.3_4
    • /
    • pp.341-354
    • /
    • 2016
  • In this paper, the exact formulae for the generalized product degree distance, reciprocal product degree distance and product degree distance of tensor product of a connected graph and the complete multipartite graph with partite sets of sizes m0, m1, ⋯ , mr−1 are obtained.

TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

  • Arslan, Kadri;Bulca, Betul;Kilic, Bengu;Kim, Young-Ho;Murathan, Cengizhan;Ozturk, Gunay
    • Bulletin of the Korean Mathematical Society
    • /
    • v.48 no.3
    • /
    • pp.601-609
    • /
    • 2011
  • Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.

STUDY ON THE TENSOR PRODUCT SPECTRUM

  • Lee, Dong Hark
    • Korean Journal of Mathematics
    • /
    • v.14 no.1
    • /
    • pp.1-5
    • /
    • 2006
  • We will introduce tensor product spectrums on the tensor product spaces. And we will show that ${\sigma}[P(T_1,T_2,{\ldots},T_n)]=P[({\sigma}(T_1),{\sigma}(T_2){\ldots},{\sigma}(T_n)]={\sigma}(T_1,T_2{\ldots},T_n)$.

  • PDF

ON THE EXTENDED HAAGERUP TENSOR PRODUCT IN OPERATOR SPACES

  • Itoh, Takashi;Nagisa, Masaru
    • Journal of the Korean Mathematical Society
    • /
    • v.51 no.2
    • /
    • pp.345-362
    • /
    • 2014
  • We describe the Haagerup tensor product ${\ell}^{\infty}{\otimes}_h{\ell}^{\infty}$ and the extended Haagerup tensor product ${\ell}^{\infty}{\otimes}_{eh}{\ell}^{\infty}$ in terms of Schur product maps, and show that ${\ell}^{\infty}{\otimes}_h{\ell}^{\infty}{\cap}\mathbb{B}({\ell}^2)$(resp. ${\ell}^{\infty}{\otimes}_{eh}{\ell}^{\infty}{\cap}\mathbb{B}({\ell}^2)$) coincides with $c_0{\otimes}_hc_0{\cap}\mathbb{B}({\ell}^2)$(resp. $c_0{\otimes}_{eh}c_0{\cap}\mathbb{B}({\ell}^2)$). For $C^*2$-algebras A, B, it is shown that $A{\otimes}_hB=A{\otimes}_{eh}B$ if and only if A or B is finite-dimensional.

SOME REDUCED FREE PRODUCTS OF ABELIAN C*

  • Heo, Jae-Seong;Kim, Jeong-Hee
    • Bulletin of the Korean Mathematical Society
    • /
    • v.47 no.5
    • /
    • pp.997-1000
    • /
    • 2010
  • We prove that the reduced free product of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras is not the minimal tensor product of reduced free products of $k\;{\times}\;k$ matrix algebras over abelian $C^*$-algebras. It is shown that the reduced group $C^*$-algebra associated with a group having the property T of Kazhdan is not isomorphic to a reduced free product of abelian $C^*$-algebras or the minimal tensor product of such reduced free products. The infinite tensor product of reduced free products of abelian $C^*$-algebras is not isomorphic to the tensor product of a nuclear $C^*$-algebra and a reduced free product of abelian $C^*$-algebra. We discuss the freeness of free product $II_1$-factors and solidity of free product $II_1$-factors weaker than that of Ozawa. We show that the freeness in a free product is related to the existence of Cartan subalgebras in free product $II_1$-factors. Finally, we give a free product factor which is not solid in the weak sense.

STUDY ON THE JOINT SPECTRUM

  • Lee, Dong Hark
    • Korean Journal of Mathematics
    • /
    • v.13 no.1
    • /
    • pp.43-50
    • /
    • 2005
  • We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

  • PDF

THE TENSOR PRODUCT OF AN ODD SPHERICAL NON-COMMUTATIVE TORUS WITH A CUNTZ ALGEBRA

  • Boo, Deok-Hoon;Park, Chun-Gil
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.11 no.1
    • /
    • pp.151-161
    • /
    • 1998
  • The odd spherical non-commutative tori $\mathbb{S}_{\omega}$ were defined in [2]. Assume that no non-trivial matrix algebra can be factored out of $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_{km}(\mathbb{C})$. It is shown that the tensor product of $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has the trivial bundle structure if and, only if km and 2d - 1 are relatively prime, and that the tensor product of $\mathbb{S}_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when km > 1.

  • PDF

THE TENSOR PRODUCTS OF SPHERICAL NON-COMMUTATIVE TORI WITH CUNTZ ALGEBRAS

  • Park, Chun-Gil;Boo, Deok-Hoon
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.10 no.1
    • /
    • pp.127-139
    • /
    • 1997
  • The spherical non-commutative $\mathbb{S}_{\omega}$ were defined in [2,3]. Assume that no non-trivial matrix algebra can be factored out of the $\mathbb{S}_{\omega}$, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra $M_k(\mathbb{C})$. It is shown that the tensor product of the spherical non-commutative torus $\mathbb{S}_{\omega}$ with the even Cuntz algebra $\mathcal{O}_{2d}$ has a trivial bundle structure if and only if k and 2d - 1 are relatively prime, and that the tensor product of the spherical non-commutative torus $S_{\omega}$ with the generalized Cuntz algebra $\mathcal{O}_{\infty}$ has a non-trivial bundle structure when k > 1.

  • PDF