In this paper we give a simple characterization of the isomorphy classes of involutions of SL(2, k) with k any field of characteristic not 2. We also classify the isomorphy classes of involutions for k algebraically closed, the real numbers, the -adic numbers and finite fields. We determine in which cases the corresponding fixed point group H is k-anisotropic. In those cases the corresponding s...

We investigate various aspects of involutions of groups, i.e, anti-automorphisms of order at most two. The emphasis is on finite abelian groups. We count the number of involutions for the cyclic groups, and consider the problem for direct products of groups. We also give a characterization for the set of skewed squares of finitely generated abelian groups with identity as the involution. The pr...

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...

Several important combinatorial arrays, after inserting some minus signs, turn out to be involutions when considered as lower triangular matrices. Among these are the Pascal, RNA, and directed animal matrices. These examples and many others are in the Bell subgroup of the Riordan group. We characterize all such pseudo-involutions by means of a single sequence called the ∆-sequence. Finally we c...

We prove the so-called Unitary Hyperbolicity Theorem, a result on hyperbolicity of unitary involutions. The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one. While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties, the proof in the unitar...

In this article we study VOAs with two Miyamoto involutions generating S3. In [M3], Miyamoto showed that a VOA generated by two conformal vectors whose Miyamoto involutions generate an automorphism group isomorphic to S3 is isomorphic to one of the four candidates he listed. We construct one of them and prove that our VOA is actually the same as VA(e, f) studied by Miyamoto.

Francis Castro, Carlos Corrada, Natalia Pacheco∗, Ivelisse Rubio, University of Puerto Rico, Ŕıo Piedras Permutations of finite fields have important applications in cryptography and coding theory. Involutions are permutations that are its own inverse and are of particular interest because the implementation used for coding can also be used for decoding. We present explicit formulas for all the...

We investigate various aspects of involutions of groups, i.e, anti-automorphisms of order at most two. The emphasis is on finite abelian groups. We count the number of involutions for the cyclic groups, and consider the problem for direct products of groups. We also give a characterization for the set of skewed squares of finitely generated abelian groups with identity as the involution. The pr...

Let In be the set of involutions in the symmetric group Sn, and for A ⊆ {0, 1, . . . , n}, let F n = {σ ∈ In | σ has a fixed points for some a ∈ A}. We give a complete characterisation of the sets A for which F n , with the order induced by the Bruhat order on Sn, is a graded poset. In particular, we prove that F {1} n (i.e., the set of involutions with exactly one fixed point) is graded, which...