• Title/Summary/Keyword: Locally compact group

Search Result 8, Processing Time 0.072 seconds

BIPROJECTIVITY OF C*r(G) AS A L1(G)-BIMODULE

  • Lee, Hun Hee
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.23 no.4
    • /
    • pp.749-755
    • /
    • 2010
  • We investigate biprojectivity of $C_{r}^{*}(G)$ as a $L^1(G)$-bimodule for a locally compact group G. The main results are the following. As a $L^1(G)$-bimodule$C_{r}^{*}(G)$ is biprojective if G is compact and is not biprojective if G is an infinite discrete group or G is a non-compact abelian group.

ON SUB-KAC ALGEBRAS AND SUBGROUPS

  • Lee, Jung-Rye
    • The Pure and Applied Mathematics
    • /
    • v.6 no.1
    • /
    • pp.1-8
    • /
    • 1999
  • Let $K_{\alpha}(G)$ (resp. $K_s(G)$) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$).

  • PDF

REDUCED CROSSED PRODUCTS BY SEMIGROUPS OF AUTOMORPHISMS

  • Jang, Sun-Young
    • Journal of the Korean Mathematical Society
    • /
    • v.36 no.1
    • /
    • pp.97-107
    • /
    • 1999
  • Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

  • PDF

ABSTRACT RELATIVE FOURIER TRANSFORMS OVER CANONICAL HOMOGENEOUS SPACES OF SEMI-DIRECT PRODUCT GROUPS WITH ABELIAN NORMAL FACTOR

  • Farashahi, Arash Ghaani
    • Journal of the Korean Mathematical Society
    • /
    • v.54 no.1
    • /
    • pp.117-139
    • /
    • 2017
  • This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

(${\tilde{\varphi}}$, ${\tilde{\psi}}$)-AMENABILITY OF L1(G)

  • Ghorbani, Zahra
    • Honam Mathematical Journal
    • /
    • v.41 no.3
    • /
    • pp.559-568
    • /
    • 2019
  • In this paper we introduce and study the concept of of (${\varphi}$, ${\psi}$)-am-enability of a locally compact group G, where ${\varphi}$ is a continuous homomorphism on G and ${\psi}:G{\rightarrow}{\mathbb{C}}$ multiplicative linear function. We prove that if the group algebra $L^1$ (G) is (${\tilde{\varphi}}$, ${\tilde{\psi}}$)-amenable then G is (${\varphi}$, ${\psi}$)-amenable, where ${\tilde{\varphi}}$ is the extension of ${\varphi}$ to M(G). In the case where ${\varphi}$ is an isomorphism on G it is shown that the converse is also valid.