Displaying similar documents to “ SU 2 nonstandard bases: case of mutually unbiased bases.”

On *-representations of U q ( s l ( 2 ) ) : more real forms

Eduard Vaysleb (1997)

Banach Center Publications

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The main goal of this paper is to do the representation-theoretic groundwork for two new candidates for locally compact (nondiscrete) quantum groups. These objects are real forms of the quantized universal enveloping algebra U q ( s l ( 2 ) ) and do not have real Lie algebras as classical limits. Surprisingly, their representations are naturally described using only bounded (in one case only two-dimensional) operators. That removes the problem of describing their Hopf structure ’on the Hilbert space...

Quantum symmetries in noncommutative C*-systems

Marcin Marciniak (1998)

Banach Center Publications

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We introduce the notion of a completely quantum C*-system (A,G,α), i.e. a C*-algebra A with an action α of a compact quantum group G. Spectral properties of completely quantum systems are investigated. In particular, it is shown that G-finite elements form the dense *-subalgebra of A. Furthermore, properties of ergodic systems are studied. We prove that there exists a unique α-invariant state ω on A. Its properties are described by a family of modular operators σ z z acting on . It turns...