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Brauer algebras and the Brauer group by Noah Schweber

By Noah Schweber

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http://www. cs. nyu. edu/faculty/davise/MathTechniques/MoreAssigs/MoreAssigs. html

Additional info for Brauer algebras and the Brauer group

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Er liefert sowohl aus der Cosinus-Gleichung als auch aus der Sinus-Gleichung das gleiche Ergebnis, namlich ' = 60ı . 9 hatte ich Sie, was eine genaue Berechnung der resultierenden Krafte betraf, auf den zweiten Abschnitt vertrostet. Jetzt kann ich mein Versprechen einlosen. Es waren drei Krafte F~1 ; F~2 ; F~3 gegeben, von denen wir wissen, da jF~1 j = 2; jF~2 j = 3 und jF~3 j = 1 gilt (ich verzichte wieder auf die Angabe der Einheit). Die Angriffswinkel betragen 0ı ; 30ı und 135ı . 9 zu addieren.

Zur Subtraktion brauchen Sie nur beide Vorgange miteinander zu kombinieren. 17. 7. Der Vektor b ragt bei dieser Konstruktion etwas verloren in die Gegend. 18 vornimmt. a b ist namlich nichts anderes als die zweite Diagonale im aufgespannten Parallelogramm. 1. Einfuhrung 33 C b D a b a–b –b –b A a a B Abb. 17. 18. Vektorsubtraktion wie es in der Skizze eingezeichnet ist. In Worten gesagt: Sie laufen b hinunter statt hinauf, um b zu erhalten, und kleben daran den Vektor a. Das Resultat ist die zweite Diagonale.

Diese Interpretation ist aber ein wenig mi verstandlich, wenn man nicht deutlich macht, da es wirklich nur auf Richtung und Lange ankommt und der Anfangspunkt egal ist. 3, mag in der Wohnung Ihrer Eltern je nach Anfangs- und Endpunkt mehr oder weniger Chaos ausgelost haben, physikalisch und mathematisch macht es keinen nennenswerten Unterschied, so lange nur Richtung und Lange gleich sind. In der Vektorrechnung interessiert man sich daher ausschlie lich fur Richtung und Lange eines Vektors. 2 Deˇnition Zwei Vektoren hei en gleich, wenn sie die gleiche Richtung und die gleiche Lange haben, das hei t, ein Vektor wird durch Richtung und Lange eindeutig bestimmt.

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