On the structure of quantum permutation groups
نویسندگان
چکیده
منابع مشابه
On the Structure of Quantum Permutation Groups
The quantum permutation group of the set Xn = {1, . . . , n} corresponds to the Hopf algebra Aaut(Xn). This is an algebra constructed with generators and relations, known to be isomorphic to C(Sn) for n ≤ 3, and to be infinite dimensional for n ≥ 4. In this paper we find an explicit representation of the algebra Aaut(Xn), related to Clifford algebras. For n = 4 the representation is faithful in...
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
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Algebraic Quantum Permutation Groups
We discuss some algebraic aspects of quantum permutation groups, working over arbitrary fields. If K is any characteristic zero field, we show that there exists a universal cosemisimple Hopf algebra coacting on the diagonal algebra K: this is a refinement of Wang’s universality theorem for the (compact) quantum permutation group. We also prove a structural result for Hopf algebras having a non-...
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A remarkable fact, discovered by Wang in [14], is that the set Xn = {1, . . . , n} has a quantum permutation group. For n = 1, 2, 3 this is the usual symmetric group Sn. However, starting from n = 4 the situation is different: for instance the dual of Z2 ∗ Z2 acts on X4. In other words, “quantum permutations” do exist. They form a compact quantum group Qn, satisfying the axioms of Woronowicz in...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-06-08464-4