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I took a quick look into Timmermann's book "An invitation to Quantum Groups".

It refers to: Saad Baaj; Georges Skandalis Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres Annales scientifiques de l'École Normale Supérieure (1993) Volume: 26, Issue: 4, page 425-488 ISSN: 0012-9593

They describe finite dimensional C${}^*$-Hopf algebras in terms of multiplicative unitaries. Theorem 2.2 shows that if you have commutative multiplicative unitaries you get a locally compact group and therefore in the finite case, a finite group.

This gives the first statement. The second statement is equivalent to the first by duality.

I took a quick look into Timmermann's book "An invitation to Quantum Groups".

It refers to:

Saad Baaj; Georges Skandalis Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres Annales scientifiques de l'École Normale Supérieure (1993) Volume: 26, Issue: 4, page 425-488 ISSN: 0012-9593

They describe finite dimensional C${}^*$-Hopf algebras in terms of multiplicative unitaries. Theorem 2.2 shows that if you have commutative multiplicative unitaries you get a locally compact group and therefore in the finite case, a finite group.

This gives the first statement. The second statement is equivalent to the first by duality.

*edit*

Such a result is already stated as Theorem 3.3 in

L. I. Vaĭnerman and G. I. Kac, Nonunimodular Ring Groups and Hopf-Von Neumann algebras, Mathematics of the USSR-Sbornik, Volume 23, Number 2

I took a quick look into Timmermann's book "An invitation to Quantum Groups".

It refers to: Saad Baaj; Georges Skandalis Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres Annales scientifiques de l'École Normale Supérieure (1993) Volume: 26, Issue: 4, page 425-488 ISSN: 0012-9593

They describe finite dimensional C${}^*$-Hopf algebras in terms of multiplicative unitaries. Theorem 2.2 shows that if you have commutative multiplicative unitaries you get a locally compact group (or in the finite case, a finite group).

This gives the first statement. The second statement is equivalent to the first by duality.

I took a quick look into Timmermann's book "An invitation to Quantum Groups".

It refers to: Saad Baaj; Georges Skandalis Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres Annales scientifiques de l'École Normale Supérieure (1993) Volume: 26, Issue: 4, page 425-488 ISSN: 0012-9593

They describe finite dimensional C${}^*$-Hopf algebras in terms of multiplicative unitaries. Theorem 2.2 shows that if you have commutative multiplicative unitaries you get a locally compact group and therefore in the finite case, a finite group.

This gives the first statement. The second statement is equivalent to the first by duality.

I took a quick look into Timmermanns book

http://archive.numdam.org/ARCHIVE/ASENS/ASENS_1993_4_26_4/ASENS_1993_4_26_4_425_0/ASENS_1993_4_26_4_425_0.pdf

I took a quick look into Timmermann's book "An invitation to Quantum Groups".

It refers to: Saad Baaj; Georges Skandalis Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres Annales scientifiques de l'École Normale Supérieure (1993) Volume: 26, Issue: 4, page 425-488 ISSN: 0012-9593

They describe finite dimensional C${}^*$-Hopf algebras in terms of multiplicative unitaries. Theorem 2.2 shows that if you have commutative multiplicative unitaries you get a locally compact group (or in the finite case, a finite group).

This gives the first statement. The second statement is equivalent to the first by duality.