ALGEBRAIC QUANTUM PERMUTATION GROUPS
نویسندگان
چکیده
منابع مشابه
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: Asian-European Journal of Mathematics
سال: 2008
ISSN: 1793-5571,1793-7183
DOI: 10.1142/s1793557108000023