InforLorV4, PascalFrancis, Curation, bibRecord, 000C47

Gauss laws in the sense of Bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups

Identifieur interne : 000C47 ( PascalFrancis/Curation ); précédent : 000C46; suivant : 000C48

Gauss laws in the sense of Bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups

Auteurs : U. Franz [France, Allemagne] ; D. Neuenschwander [Suisse] ; R. Schott [France]

Source :

Probability theory and related fields [ 0178-8051 ] ; 1997.

RBID : Pascal:97-0494440

Descripteurs français

Pascal (Inist)
- Plongement, Semigroupe, Groupe quantique, Loi probabilité, Groupe Heisenberg, Groupe Weyl, Suite variable aléatoire, Groupe Lie, Algèbre Hopf, 81R50, Unicité plongement, Propriété Bernstein, Groupe nilpotent, Groupe connexe, Propriété Poincré Birkhoff Witt, Loi Gauss, Groupe convolution, Groupe tressé, Fonctionnelle Gauss.

English descriptors

KwdEn :
- Braided group, Convolution group, Embedding, Gauss law, Gaussian functional, Heisenberg group, Hopf algebra, Lie group, Probability distribution, Quantum group, Random variable sequence, Semigroup, Weyl group.

Abstract

The goal of this paper is to characterise certain probability laws on a class of quantum groups or braided groups that we will call nilpotent. First we introduce a braided analogue of the Heisenberg-Weyl group, which shall serve as standard example. We introduce Gaussian functionals on quantum groups or braided groups as functionals that satisfy an analogue of the Bernstein property, i.e. that the sum and difference of independent random variables are also independent. The corresponding functionals on the braided line, braided plane and a braided q-Heisenberg-Weyl group are determined. Section 5 deals with continuous convolution semigroups on nilpotent quantum groups and braided groups. We extend recent results proving the uniqueness of the embedding of an infinitely divisible probability law into a continuous convolution semigroup for simply connected nilpotent Lie groups to nilpotent quantum groups and braided groups. Finally, in Section 6 we give some indications how the semigroup approach of Heyer and Hazod to the Bernstein theorem on groups can be extended to quantum groups and braided groups.

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C03	`08`	`X`	`SPA`	`@0 Grupo Lie @5 08`
C03	`09`	`X`	`FRE`	`@0 Algèbre Hopf @5 09`
C03	`09`	`X`	`ENG`	`@0 Hopf algebra @5 09`
C03	`09`	`X`	`SPA`	`@0 Algebra Hopf @5 09`
C03	`10`	`X`	`FRE`	`@0 81R50 @4 INC @5 28`
C03	`11`	`X`	`FRE`	`@0 Unicité plongement @4 INC @5 75`
C03	`12`	`X`	`FRE`	`@0 Propriété Bernstein @4 INC @5 76`
C03	`13`	`X`	`FRE`	`@0 Groupe nilpotent @4 INC @5 77`
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N21				`@1 300`

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<front><div type="abstract" xml:lang="en">The goal of this paper is to characterise certain probability laws on a class of quantum groups or braided groups that we will call nilpotent. First we introduce a braided analogue of the Heisenberg-Weyl group, which shall serve as standard example. We introduce Gaussian functionals on quantum groups or braided groups as functionals that satisfy an analogue of the Bernstein property, i.e. that the sum and difference of independent random variables are also independent. The corresponding functionals on the braided line, braided plane and a braided q-Heisenberg-Weyl group are determined. Section 5 deals with continuous convolution semigroups on nilpotent quantum groups and braided groups. We extend recent results proving the uniqueness of the embedding of an infinitely divisible probability law into a continuous convolution semigroup for simply connected nilpotent Lie groups to nilpotent quantum groups and braided groups. Finally, in Section 6 we give some indications how the semigroup approach of Heyer and Hazod to the Bernstein theorem on groups can be extended to quantum groups and braided groups.</div>
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</fC03>
<fC03 i1="15" i2="X" l="FRE"><s0>Propriété Poincré Birkhoff Witt</s0>
<s4>INC</s4>
<s5>79</s5>
</fC03>
<fC03 i1="16" i2="X" l="FRE"><s0>Loi Gauss</s0>
<s4>CD</s4>
<s5>96</s5>
</fC03>
<fC03 i1="16" i2="X" l="ENG"><s0>Gauss law</s0>
<s4>CD</s4>
<s5>96</s5>
</fC03>
<fC03 i1="17" i2="X" l="FRE"><s0>Groupe convolution</s0>
<s4>CD</s4>
<s5>97</s5>
</fC03>
<fC03 i1="17" i2="X" l="ENG"><s0>Convolution group</s0>
<s4>CD</s4>
<s5>97</s5>
</fC03>
<fC03 i1="18" i2="X" l="FRE"><s0>Groupe tressé</s0>
<s4>CD</s4>
<s5>98</s5>
</fC03>
<fC03 i1="18" i2="X" l="ENG"><s0>Braided group</s0>
<s4>CD</s4>
<s5>98</s5>
</fC03>
<fC03 i1="19" i2="X" l="FRE"><s0>Fonctionnelle Gauss</s0>
<s4>CD</s4>
<s5>99</s5>
</fC03>
<fC03 i1="19" i2="X" l="ENG"><s0>Gaussian functional</s0>
<s4>CD</s4>
<s5>99</s5>
</fC03>
<fN21><s1>300</s1>
</fN21>
</pA>
</standard>
</inist>
</record>

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Gauss laws in the sense of Bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups

Gauss laws in the sense of Bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups

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