Induced corepresentations of locally compact quantum groups
نویسنده
چکیده
Consider a closed subgroup H of a locally compact group G together with a strongly continuous unitary representation u of H on a Hilbert space K. The construction of the induced representation uses these three ingredients to supply a new strongly continuous unitary representation ρ of the larger group G on a new Hilbert space K. Induced group representations for finite groups where first introduced by Frobenius in 1898. The theory of induced representations for locally compact groups was initiated by Mackey in 1949 (see [14], [15] and [16]). He restricted himself to locally compact groups satisfying the second axiom of countability and separable Hilbert spaces. The general case was treated by Blattner in 1961 (see [3]). The role of the theory of induced representations in the classical theory of locally compact groups can hardly be underestimated. This construction is for instance one of the primary instruments to construct the different series of special representations of various non-compact locally compact groups.
منابع مشابه
Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
متن کامل
Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
متن کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کامل2-Groups, trialgebras and their Hopf categories of representations
A strict 2-group is a 2-category with one object in which all morphisms and all 2morphisms have inverses. 2-Groups have been studied in the context of homotopy theory, higher gauge theory and Topological Quantum Field Theory (TQFT). In the present article, we develop the notions of trialgebra and cotrialgebra, generalizations of Hopf algebras with two multiplications and one comultiplication or...
متن کاملThe similarity problem for Fourier algebras and corepresentations of group von Neumann algebras
Let G be a locally compact group, and let A(G) and VN(G) be its Fourier algebra and group von Neumann algebra, respectively. In this paper we consider the similarity problem for A(G): Is every bounded representation of A(G) on a Hilbert space H similar to a ∗-representation? We show that the similarity problem for A(G) has a negative answer if and only if there is a bounded representation of A(...
متن کامل