Twisting
The property of being a quasi-triangular Hopf algebra is preserved by twisting via an invertible element such that and satisfying the cocycle condition
Furthermore, is invertible and the twisted antipode is given by, with the twisted comultiplication, R-matrix and co-unit change according to those defined for the quasi-triangular Quasi-Hopf algebra. Such a twist is known as an admissible (or Drinfel'd) twist.
Read more about this topic: Quasitriangular Hopf Algebra
Famous quotes containing the word twisting:
“... So damn your food and damn your wines,
Your twisted loaves and twisting vines,
Your table d’hôte, your à la carte,
. . . .
From now on you can keep the lot.
Take every single thing you’ve got,
Your land, your wealth, your men, your dames,
Your dream of independent power,
And dear old Konrad Adenauer,
And stick them up your Eiffel Tower.”
—Anthony Jay (b. 1930)
“Jesus was all right, but his disciples were thick and ordinary. It’s them twisting it that ruins it for me.”
—John Lennon (1940–1980)
“Farmers in overalls and wide-brimmed straw hats lounge about the store on hot summer days, when the most common sound is the thump-thump-thump of a hound’s leg on the floor as he scratches contentedly. Oldtime hunters say that fleas are a hound’s salvation: his constant twisting and clawing in pursuit of the tormentors keeps his joints supple.”
—Administration in the State of Arka, U.S. public relief program (1935-1943)