A New Quantum Group Associated with a 'Nonstandard ' Braid Group Representation

Abstract. A new quantum group is derived from a 'nonstandard ' braid group representation by employing the Faddeev-Reshetlkhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like.,c 2 =)' ~ = 0. We classify all finite-dimensional irreducible representa-tions of the new Hopf algebra and find only one- and two-dimensional ones. AMS subject classifications (1980). 16A24, 17B55, 20GXX, 22E65. I