Topological centres for group algebras actions and quantum groups

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Topological centres for group algebras, actions, and quantum groups Matthias Neufang Carleton University (Ottawa)

  • canonical extensions

  • quantum group

  • ?? a??

  • arens products

  • y2f ?

  • algebraic description


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Langue English
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Topological centres for group algebras,
actions, and quantum groups
Matthias Neufang
Carleton University (Ottawa)Topological centre basics Topological centre problems Topological centres as a tool
1 Topological centre basics
2 Topological centre problems
3 Topological centres as a toolTopological centre basics Topological centre problems Topological centres as a tool
1 Topological centre basics
2 Topological centre problems
3 Topological centres as a toolA Banach algebra; as Banach space:A,!A
9 2 canonical extensions of product toA (Arens ’51)
X; Y2A , f2A , a; b2A
hX2Y; fi = hX; Y2fi
hY2f; ai = hY; f2ai
hf2a; bi = hf; a bi
. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description9 2 canonical extensions of product toA (Arens ’51)
X; Y2A , f2A , a; b2A
hX2Y; fi = hX; Y2fi
hY2f; ai = hY; f2ai
hf2a; bi = hf; a bi
. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description
A Banach algebra; as Banach space:A,!A X; Y2A , f2A , a; b2A
hX2Y; fi = hX; Y2fi
hY2f; ai = hY; f2ai
hf2a; bi = hf; a bi
. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description
A Banach algebra; as Banach space:A,!A
9 2 canonical extensions of product toA (Arens ’51)hX2Y; fi = hX; Y2fi
hY2f; ai = hY; f2ai
hf2a; bi = hf; a bi
. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description
A Banach algebra; as Banach space:A,!A
9 2 canonical extensions of product toA (Arens ’51)
X; Y2A , f2A , a; b2AhY2f; ai = hY; f2ai
hf2a; bi = hf; a bi
. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description
A Banach algebra; as Banach space:A,!A
9 2 canonical extensions of product toA (Arens ’51)
X; Y2A , f2A , a; b2A
hX2Y; fi = hX; Y2fihf2a; bi = hf; a bi
. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description
A Banach algebra; as Banach space:A,!A
9 2 canonical extensions of product toA (Arens ’51)
X; Y2A , f2A , a; b2A
hX2Y; fi = hX; Y2fi
hY2f; ai = hY; f2ai. . . and the other way around:
hX3Y; fi = hY; f3Xi
hf3X; ai = hX; a3fi
ha3f; bi = hf; b ai
Topological centre basics Topological centre problems Topological centres as a tool
Arens products: Algebraic description
A Banach algebra; as Banach space:A,!A
9 2 canonical extensions of product toA (Arens ’51)
X; Y2A , f2A , a; b2A
hX2Y; fi = hX; Y2fi
hY2f; ai = hY; f2ai
hf2a; bi = hf; a bi