6 papers
Braided Lie algebras and bicovariant differential calculi over coquasitriangular Hopf algebras
X. Gomez, S. Majid
We show that if is the quantum tangent space (or quantum Lie algebra in the sense of Woronowicz) of a bicovariant first order differential calculus over a coquasitriangular H…
Braided Line and Counting Fixed Points of GL(d,F_q)
P. J. Cameron, S. Majid
We interpret a recent formula for counting orbits of in terms of counting fixed points as addition in the affine braided line. The theory of such braided groups (or Hop…
Clifford algebras obtained by twisting of group algebras
H. Albuquerque, S. Majid
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2…
Noncommutative Differential Geometry and Twisting of Quantum Groups
S. Majid
We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riem…
Quantum geometry of algebra factorisations and coalgebra bundles
Tomasz Brzezinski, Shahn Majid
We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=…
Quasialgebra structure of the octonions
H. Albuquerque, S. Majid
We show that the octonions are a twisting of the group algebra of Z_2 x Z_2 x Z_2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-coc…