Dilating Covariant Representations of the Non-commutative Disc Algebras
نویسندگان
چکیده
Let φ be an isometric automorphism of the non-commutative disc algebra An for n ≥ 2. We show that every contractive covariant representation of (An, φ) dilates to a unitary covariant representation of (On, φ). Hence the C*-envelope of the semicrossed product An ×φ Z is On ×φ Z.
منابع مشابه
Universal Central Extension of Current Superalgebras
Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras are very impo...
متن کاملTowards Gauge theory for a class of commutative and non-associative fuzzy spaces
We discuss gauge theories for commutative but non-associative algebras related to the SO(2k + 1) covariant finite dimensional fuzzy 2k-sphere algebras. A consequence of non-associativity is that gauge fields and gauge parameters have to be generalized to be functions of coordinates as well as derivatives. The usual gauge fields depending on coordinates only are recovered after a partial gauge f...
متن کاملCommutative pseudo BE-algebras
The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...
متن کاملHomomorphism Weak amenability of certain Banach algebras
In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...
متن کاملNon-Commutative Harmonic Analysis
For present purposes, we shall define non-commutative harmonic analysis to mean the decomposition of functions on a locally compact G-space X,1 where G is some (locally compact) group, into functions well-behaved with respect to the action of G. The classical cases are of course Fourier series, when G = X = T, the circle group, and the Fourier transform, when G = X = R, but we will mostly be co...
متن کامل