The Baer-Invariant and the Direct Limit.
The Balance of Tor.
The Banach-Tarski paradox for the hyperbolic plane (II)
The second author found a gap in the proof of the main theorem in [J. Mycielski, Fund. Math. 132 (1989), 143-149]. Here we fill that gap and add some remarks about the geometry of the hyperbolic plane ℍ².
The based ring of the lowest two-sided cell of an affine Weyl group. II
The basic construction from the conditional expectation on the quantum double of a finite group
Let be a finite group and a subgroup. Denote by (or ) the crossed product of and (or ) with respect to the adjoint action of the latter on the former. Consider the algebra generated by and , where we regard as an idempotent operator on for a certain conditional expectation of onto . Let us call the basic construction from the conditional expectation . The paper constructs a crossed product algebra , and proves that there is an algebra isomorphism between and .
The Bass conjecture and growth in groups
We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.
The Bauer trees of the exceptional Chevalley groups of type E6.
The bicommutator of the injective hull of a nonsingular semigroup.
The bicyclic semigroup has F4*.
The bifree regular E-solid semigroups.
The Birkhoff-Neumann Embedding of Relatively Free Groups
The blocks of finite classical groups.
The Blocks of Finite General Linear and Unitary Groups.
The bounded model for hyperbolic 3-space and a quaternionic uniformization theorem.
The box-counting dimension for geometrically finite Kleinian groups
We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the 'global measure formula' for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we conclude that for a geometrically finite group these three different types of dimension coincide with the...
The braid groups of the projective plane.
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The Brauer group of integral group rings.
The Brauer tree of the principal 19-block of the sporadic simple Thompson group.
The Burau representation is not faithful for .