منابع مشابه
Simple Compact Quantum Groups I
The notion of simple compact quantum group is introduced. As non-trivial (noncommutative and noncocommutative) examples, the following families of compact quantum groups are shown to be simple: (a) The universal quantum groups Bu(Q) for Q ∈ GL(n,C) satisfying QQ̄ = ±In, n ≥ 2; (b) The quantum automorphism groups Aaut(B, τ) of finite dimensional C ∗-algebras B endowed with the canonical trace τ w...
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We study the (compact) quantum subgroups of the compact quantum group SU−1(3): we show that any non-classical such quantum subgroup is a twist of a compact subgroup of SU(3) or is isomorphic to a quantum subgroup of U−1(2).
متن کاملgalois extension for a compact quantum group
The aim of this paper is to introduce the quantum analogues of torsors for a compact quantum group and to investigate their relations with representation theory. Let A be a Hopf algebra over a field k. A theorem of Ulbrich asserts that there is an equivalence of categories between neutral fibre functors on the category of finitedimensional A-comodules and A-Galois extensions of k. We give the c...
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We generalise the quantum double construction of Drinfel’d to the case of the (Hopf) algebra of suitable functions on a compact or locally compact group. We will concentrate on the ∗-algebra structure of the quantum double. If the conjugacy classes in the group are countably separated, then we classify the irreducible ∗-representations by using the connection with so–called transformation group...
متن کاملThe Haar Measure on a Compact Quantum Group
Let A be a C*-algebra with an identity. Consider the completed tensor product A®A of A with itself with respect to the minimal or the maximal C*-tensor product norm. Assume that A: A —>A®A is a non-zero •-homomorphism such that (A ® t)A = (i ® A)A where / is the identity map. Then A is called a comultiplication on A . The pair (A, A) can be thought of as a 'compact quantum semi-group'. A left i...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.06.004