We prove the Goldman-Parker Conjecture: A complex hyperbolic ideal triangle group is discretely embedded in PU(2, 1) if and only if the product of its three standard generators is not elliptic. We also prove that such a group is indiscrete if the product of its three standard generators is elliptic. A novel feature of this paper is that it uses a rigorous computer assisted proof to deal with di...

Define the growth function γ associated with a finitely generated group and a specified choice of generators {gl7 -, gp} for the group as follows (compare [9]). For each positive integer s let γ(s) be the number of distinct group elements which can be expressed as words of length < s in the specified generators and their inverses. (For example, if the group is free abelian of rank 2 with specif...

We define the dual of a set of generators of the fundamental group of an oriented two-surface S g,n of genus g with n punctures and the associated surface S g,n \D with a disc D removed. This dual is another set of generators related to the original generators via an involution and has the properties of a dual graph. In particular, it provides an algebraic prescription for determining the inter...

We derive expressions for Poincaré group generators using preturbative similarity renormalization group procedure for Hamiltonians. We show that generators obtained in second-order perturbation theory satisfy required commutation relations in weak sense, i.e. in matrix elements between states of finite invariant masses. ∗Talk to be delivered at 12th Nuclear Physics Summer School and Symposium “...

The following question was asked by V. V. Bludov in The Kourovka Notebook in 1995: If a torsion-free group G has a finite system of generators a1, . . . , an such that every element of G has a unique presentation in the form a k1 1 · · · a kn n where ki ∈ Z, is it true that G is virtually polycyclic? The answer is “not always.” A counterexample is constructed in this paper as a group presented ...

Abstract. A few things are known, and many are unknown, on the automorphism group of the free MV-algebra over n − 1 generators. In this paper we show that this group appears as the stabilizer of 1l in the larger group of all automorphisms of the free cancellative hoop over n generators. Both groups have a dual action on the same space, namely the (n − 1)-dimensional cube. The larger group has a...

We consider the radial quantization of N = 4 super Yang-Mills (SYM) in 4 dimensions, i.e., N = 4 SYM on a cylinder R × S 3. We construct the generators of superconformal symmetry in the case of U (N) gauge group, generalizing the earlier work by Nicolai et al. for U (1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.

We consider the radial quantization of N = 4 super Yang-Mills (SYM) in 4 dimensions, i.e., N = 4 SYM on a cylinder R × S 3. We construct the generators of superconformal symmetry in the case of U (N) gauge group, generalizing the earlier work by Nicolai et al. for U (1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.

We consider the radial quantization of N = 4 super Yang-Mills (SYM) in 4 dimensions, i.e., N = 4 SYM on a cylinder R × S 3. We construct the generators of superconformal symmetry in the case of U (N) gauge group, generalizing the earlier work by Nicolai et al. for U (1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.

Abstract. We use the free entropy defined by D. Voiculescu to prove that the free group factors can not be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian ∗-subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hyperfinite and abelian dimensions of free group...